تكلم مع الذكاء الاصطناعي
Deck 3: Polynomial and Rational Functions
ملء الشاشة (f)
سؤال
Find an equation of the parabola that has a vertex at 
and whose graph passes through the point 
A)
B)
C)
D)
E)
and whose graph passes through the point A)
B)
C)
D)
E)
سؤال
Find all real zeros of the polynomial 
and determine the mutiplicity of each.
A)
, multiplicity 2; 
, multiplicity 2
B)
, multiplicity 2; 
, multiplicity 2
C)
, multiplicity 2; 
, multiplicity 1
D)
, multiplicity 2; 
, multiplicity 2
E)
, multiplicity 1; 
, multiplicity 1; 
, multiplicity 1; 
, multiplicity 1
and determine the mutiplicity of each.A)
, multiplicity 2; , multiplicity 2B)
, multiplicity 2; , multiplicity 2C)
, multiplicity 2; , multiplicity 1D)
, multiplicity 2; , multiplicity 2E)
, multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1 سؤال
Match the equation with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Describe the right-hand and the left-hand behavior of the graph of 
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
سؤال
Determine the vertex of the graph of the quadratic function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Describe the right-hand and the left-hand behavior of the graph of 
A) Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right.
B) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right.
D) Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.
E) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.
A) Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right.
B) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right.
D) Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.
E) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.
سؤال
The sum of the length l and the width w of a rectangular region is 180 meters.Write the area A as a function of l.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below. 
Find a quadratic model for these data.
A)
B)
C)
D)
E)
Find a quadratic model for these data.A)
B)
C)
D)
E)
سؤال
A farmer has 288 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Determine the vertex of the graph of the quadratic function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all real zeros of the polynomial 
and determine the mutiplicity of each.
A)
, multiplicity 2; 
, multiplicity 1; 
, multiplicity 1
B)
, multiplicity 2; 
, multiplicity 2
C)
, multiplicity 2; 
, multiplicity 1; 
, multiplicity 1
D)
, multiplicity 2; 
, multiplicity 2
E)
, multiplicity 1; 
, multiplicity 1; 
, multiplicity 1; 
, multiplicity 1
and determine the mutiplicity of each.A)
, multiplicity 2; , multiplicity 1; , multiplicity 1B)
, multiplicity 2; , multiplicity 2C)
, multiplicity 2; , multiplicity 1; , multiplicity 1D)
, multiplicity 2; , multiplicity 2E)
, multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1 سؤال
Graph the given function. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Describe the right-hand and the left-hand behavior of the graph of 
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.
سؤال
The sum of the length l and the width w of a rectangular region is 190 meters.Find the dimensions that produce the greatest area.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The height in feet of a projectile with an initial velocity of 96 feet per second and an initial height of 75 feet is a function of time t, in seconds, given by 
Find the maximum height of the projectile.
A) 254 ft
B) 219 ft
C) 263 ft
D) 105 ft
E) 315 ft
Find the maximum height of the projectile.A) 254 ft
B) 219 ft
C) 263 ft
D) 105 ft
E) 315 ft
سؤال
The path of a diver is given by 
where 
is the height (in feet) and 
is the horizontal distance from the end of the diving board (in feet).Find the maximum height of the diver.
A) 12 feet
B) 13 feet
C) 10 feet
D) 14 feet
E) 17 feet
where is the height (in feet) and is the horizontal distance from the end of the diving board (in feet).Find the maximum height of the diver.A) 12 feet
B) 13 feet
C) 10 feet
D) 14 feet
E) 17 feet
سؤال
Compare the graph of 
with 
A)
shifts right 
units, shifts downward 
units, and shrinks by a factor of 
B)
shifts right 
units, shifts upward 
units, and stretches by a factor of 
C)
shifts left 
units, shifts downward 
units, and stretches by a factor of 
D)
shifts right 
units, shifts upward 
units, and shrinks by a factor of 
E)
shifts left 
units, shifts upward 
units, and stretches by a factor of 
with A)
shifts right units, shifts downward units, and shrinks by a factor of B)
shifts right units, shifts upward units, and stretches by a factor of C)
shifts left units, shifts downward units, and stretches by a factor of D)
shifts right units, shifts upward units, and shrinks by a factor of E)
shifts left units, shifts upward units, and stretches by a factor of سؤال
Examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function 
A) down to the far left, up to the far right
B) down to the far left, down to the far right
C) up to the far left, up to the far right
D) up to the far left, down to the far right
E) cannot be determined
A) down to the far left, up to the far right
B) down to the far left, down to the far right
C) up to the far left, up to the far right
D) up to the far left, down to the far right
E) cannot be determined
سؤال
The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below. 
Find a quadratic model for these data and use it to predict the fuel efficiency of this car when it is traveling at a speed of 40 mph.Do not round any values in your calculations but round the final answer to the nearest tenth.
A) 33.9 mpg
B) 33.7 mpg
C) 35.7 mpg
D) 32.7 mpg
E) 33.9 mpg
Find a quadratic model for these data and use it to predict the fuel efficiency of this car when it is traveling at a speed of 40 mph.Do not round any values in your calculations but round the final answer to the nearest tenth.A) 33.9 mpg
B) 33.7 mpg
C) 35.7 mpg
D) 32.7 mpg
E) 33.9 mpg
سؤال
Find an equation of the parabola below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write 
in the form 
when 
A)
B)
C)
D)
E)
in the form when A)
B)
C)
D)
E)
سؤال
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use long division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use long division to divide the first polynomial below by the second. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Using the factors 
and 
, find the remaining factor(s) of 
and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
سؤال
Find all the real zeros of the polynomial function 
and determine the multiplicity of each.
A)
, multiplicity 2; 
, multiplicity 1
B)
, multiplicity 1; 
, multiplicity 1; 
, multiplicity 1
C)
, multiplicity 2; 
, multiplicity 1
D)
, multiplicity 1; 
, multiplicity 1; 
, multiplicity 1
E)
, multiplicity 3
and determine the multiplicity of each.A)
, multiplicity 2; , multiplicity 1B)
, multiplicity 1; , multiplicity 1; , multiplicity 1C)
, multiplicity 2; , multiplicity 1D)
, multiplicity 1; , multiplicity 1; , multiplicity 1E)
, multiplicity 3 سؤال
Use synthetic division to divide 
by 
A)
B)
C)
D)
E)
by A)
B)
C)
D)
E)
سؤال
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Using the factors 
and 
, find the remaining factor(s) of 
and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
سؤال
A closed box is to be constructed from a rectangular sheet of cardboard that measures 57 inches by 28 inches.The box is made by cutting rectangles that measure x inches by 2x inches from two of the corners and by cutting two squares that measure x inches by x inches from the top and from the bottom of the rectangle, as shown in the following figure.Use a graphing calculator to determine what value of x (to the nearest thousandth of an inch) will produce a box with maximum volume? 
A) 5.314
B) 21.000
C) 4.222
D) 16.686
E) 3.707
A) 5.314
B) 21.000
C) 4.222
D) 16.686
E) 3.707
سؤال
Use synthetic division and the Factor Theorem to determine whether or not 
is a factor of 
A) Yes,
is a factor.
B) No,
is not a factor.
is a factor of A) Yes,
is a factor.B) No,
is not a factor. سؤال
Use synthetic division and the Factor Theorem to determine whether or not 
is a factor of 
A) No,
is not a factor.
B) Yes,
is a factor.
is a factor of A) No,
is not a factor.B) Yes,
is a factor. سؤال
Sketch the graph of the polynomial function 
Do not use a graphing calculator.
A)
B)
C)
D)
E)
Do not use a graphing calculator.A)
B)
C)
D)
E)
سؤال
Match the graph with one of the following functions below. 
Function I : 
Function II : 
Function III : 
Function IV : 
Function V : 
A) Function I
B) Function IV
C) Function V
D) Function II
E) Function III
Function I : Function II : Function III : Function IV : Function V : A) Function I
B) Function IV
C) Function V
D) Function II
E) Function III
سؤال
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Sketch the graph of the polynomial function below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use synthetic division to divide. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find the real zeros of the polynomial function 
and determine the multiplicity of each.
A)
, multiplicity 2; 
, multiplicity 3
B)
, multiplicity 2; 
, multiplicity 1; 
, multiplicity 2
C)
, multiplicity 3; 
, multiplicity 2
D)
, multiplicity 3; 
, multiplicity 2
E)
, multiplicity 2; 
, multiplicity 2; 
, multiplicity 1
and determine the multiplicity of each.A)
, multiplicity 2; , multiplicity 3B)
, multiplicity 2; , multiplicity 1; , multiplicity 2C)
, multiplicity 3; , multiplicity 2D)
, multiplicity 3; , multiplicity 2E)
, multiplicity 2; , multiplicity 2; , multiplicity 1 سؤال
If 
, use synthetic division to evaluate 
A)
B)
C)
D)
E)
, use synthetic division to evaluate A)
B)
C)
D)
E)
سؤال
Simplify the rational expression, 
, by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
سؤال
Find all the rational zeros of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write the complex number 
in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
سؤال
Find the zeros of the polynomial function below.If a zero is a multiple zero, state its multiplicity. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all real solutions of the polynomial equation 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Use the Rational Zero Test to list all possible rational zeros of the polynomial function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Simplify the rational expression, 
, by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
سؤال
Find all the real zeros of 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all real solutions of the polynomial equation 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
سؤال
An open box is to be made from a square piece of cardboard, 72 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).After determining the function V, in terms of x, that represents the volume of the box, use a graphing utility to estimate the dimensions that will maximize its volume. 
A)
× 
× 
B)
× 
× 
C)
× 
× 
D)
× 
× 
E)
× 
× 
A)
× × B)
× × C)
× × D)
× × E)
× × سؤال
Find all the rational zeros of the function 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write the complex number in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Evaluate the power of i. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height. If the volume of the box is 440 cubic inches, find the dimensions of the box. 
A) 5 in. by 11 in. by 8 in.
B) 4 in. by 9 in. by 7 in.
C) 109 in. by 219 in. by 112 in.
D) 5.5 in. by 12 in. by 8.5 in.
E) 106 in. by 213 in. by 109 in.
A) 5 in. by 11 in. by 8 in.
B) 4 in. by 9 in. by 7 in.
C) 109 in. by 219 in. by 112 in.
D) 5.5 in. by 12 in. by 8.5 in.
E) 106 in. by 213 in. by 109 in.
سؤال
Find real numbers a and b such that the equation 
is true.
A)
B)
C)
D)
E)
is true.A)
B)
C)
D)
E)
سؤال
Use the zero or root feature of a graphing utility to approximate the real zeros of the function 
accurate to the nearest thousandth.
A)
, 1.732, 1.414
B) -1.732, -1.414
C)
1.732, 
1.414
D) 1.732, 1.414
E)
, - 1.732, 1.414
accurate to the nearest thousandth.A)
, 1.732, 1.414B) -1.732, -1.414
C)
1.732, 1.414D) 1.732, 1.414
E)
, - 1.732, 1.414 سؤال
Use the Rational Zero Test to list possible rational zeros for the polynomial function below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Find all the real zeros of 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
A company that produces video games estimates that the profit 
(in dollars) for selling a new game is given by 
where 
is the advertising expense (in tens of thousands of dollars).Using this model, how much should the company spend on advertising to obtain a profit of $6,500,000? Round to the nearest dollar.
A) $399,893 or $744,397
B) $433,844 or $721,190
C) $315,902 or $794,255
D) $368,914 or $764,017
E) $344,417 or $778,509
(in dollars) for selling a new game is given by where is the advertising expense (in tens of thousands of dollars).Using this model, how much should the company spend on advertising to obtain a profit of $6,500,000? Round to the nearest dollar.A) $399,893 or $744,397
B) $433,844 or $721,190
C) $315,902 or $794,255
D) $368,914 or $764,017
E) $344,417 or $778,509
سؤال
Simplify and write the following complex number in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Combine 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
سؤال
Simplify and write the following complex number in standard form. 
A)
B)
C)
D)
E) 0
A)
B)
C)
D)
E) 0
سؤال
Use the quadratic formula to solve 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Write the polynomial 
as the product of factors that are irreducible over the rationals.
A)
B)
C)
D)
E)
as the product of factors that are irreducible over the rationals.A)
B)
C)
D)
E)
سؤال
Simplify 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
سؤال
Simplify 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
سؤال
Simplify 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
سؤال
Classify whether the following numbers are in the Mandelbrot Set. I : 
II : 
III : 
A) Only numbers I and III are in the Mandelbrot Set.
B) Only number II is in the Mandelbrot Set.
C) Only number I is in the Mandelbrot Set.
D) None are in the Mandelbrot Set.
E) Only numbers II and III are in the Mandelbrot Set.
II : III : A) Only numbers I and III are in the Mandelbrot Set.
B) Only number II is in the Mandelbrot Set.
C) Only number I is in the Mandelbrot Set.
D) None are in the Mandelbrot Set.
E) Only numbers II and III are in the Mandelbrot Set.
سؤال
Write the following expression as a complex number in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Simplify and write the following complex number in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
Simplify 
and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
سؤال
Write 
as a product of linear factors given that 
and 
are zeros of the polynomial.
A)
B)
C)
D)
E)
as a product of linear factors given that and are zeros of the polynomial.A)
B)
C)
D)
E)
سؤال
Find all the zeros of the polynomial function 
and write the polynomial as a product of its linear factors.
A)
, 
, 
; 
B)
, 
, 
; 
C)
, 
, 
; 
D)
, 
, 
; 
E)
, 
, 
; 
and write the polynomial as a product of its linear factors.A)
, , ; B)
, , ; C)
, , ; D)
, , ; E)
, , ; سؤال
Plot the complex number below. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The demand and cost equations for a stethoscope are given by 
and 
where 
is the unit price (in dollars), 
is the total cost (in dollars), and 
is the number of units.The total profit 
(in dollars) obtained by producing and selling 
units is given by 
Determine a price 
that would yield a profit of $4 million.
A) $22.21
B) $44.43
C) $88.85
D) $99.96
E) $66.64
and where is the unit price (in dollars), is the total cost (in dollars), and is the number of units.The total profit (in dollars) obtained by producing and selling units is given by Determine a price that would yield a profit of $4 million.A) $22.21
B) $44.43
C) $88.85
D) $99.96
E) $66.64
سؤال
Determine the number of zeros of the polynomial function below. 
A) 1
B) 3
C) 4
D) 5
E) 6
A) 1
B) 3
C) 4
D) 5
E) 6
سؤال
Write 
as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
سؤال
Write 
as a product of linear factors given that 
and 
are zeros of the polynomial.
A)
B)
C)
D)
E)
as a product of linear factors given that and are zeros of the polynomial.A)
B)
C)
D)
E)
سؤال
Simplify and write the following complex number in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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ملء الشاشة (f)
Deck 3: Polynomial and Rational Functions
1
Find an equation of the parabola that has a vertex at and whose graph passes through the point
A)
B)
C)
D)
E)
and whose graph passes through the point A)
B)
C)
D)
E)
B
2
Find all real zeros of the polynomial and determine the mutiplicity of each.
A) , multiplicity 2; , multiplicity 2
B) , multiplicity 2; , multiplicity 2
C) , multiplicity 2; , multiplicity 1
D) , multiplicity 2; , multiplicity 2
E) , multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1
and determine the mutiplicity of each.A)
, multiplicity 2; , multiplicity 2B)
, multiplicity 2; , multiplicity 2C)
, multiplicity 2; , multiplicity 1D)
, multiplicity 2; , multiplicity 2E)
, multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1E
3
Match the equation with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
E
4
Describe the right-hand and the left-hand behavior of the graph of
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
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5
Determine the vertex of the graph of the quadratic function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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6
Describe the right-hand and the left-hand behavior of the graph of
A) Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right.
B) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right.
D) Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.
E) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.
A) Because the degree is even and the leading coefficient is negative, the graph falls to the left and falls to the right.
B) Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.
C) Because the degree is even and the leading coefficient is negative, the graph falls to the left and rises to the right.
D) Because the degree is even and the leading coefficient is negative, the graph rises to the left and rises to the right.
E) Because the degree is odd and the leading coefficient is negative, the graph rises to the left and rises to the right.
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7
The sum of the length l and the width w of a rectangular region is 180 meters.Write the area A as a function of l.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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8
The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below. Find a quadratic model for these data.
A)
B)
C)
D)
E)
Find a quadratic model for these data.A)
B)
C)
D)
E)
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9
A farmer has 288 feet of fencing and wants to build two identical pens for his prize-winning pigs.The pens will be arranged as shown.Determine the dimensions of a pen that will maximize its area.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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10
Determine the vertex of the graph of the quadratic function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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11
Find all real zeros of the polynomial and determine the mutiplicity of each.
A) , multiplicity 2; , multiplicity 1; , multiplicity 1
B) , multiplicity 2; , multiplicity 2
C) , multiplicity 2; , multiplicity 1; , multiplicity 1
D) , multiplicity 2; , multiplicity 2
E) , multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1
and determine the mutiplicity of each.A)
, multiplicity 2; , multiplicity 1; , multiplicity 1B)
, multiplicity 2; , multiplicity 2C)
, multiplicity 2; , multiplicity 1; , multiplicity 1D)
, multiplicity 2; , multiplicity 2E)
, multiplicity 1; , multiplicity 1; , multiplicity 1; , multiplicity 1 فتح الحزمة
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12
Graph the given function.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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13
Describe the right-hand and the left-hand behavior of the graph of
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.
A) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right.
B) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and falls to the right.
C) Because the degree is odd and the leading coefficient is positive, the graph falls to the left and rises to the right.
D) Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right.
E) Because the degree is even and the leading coefficient is positive, the graph rises to the left and rises to the right.
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14
The sum of the length l and the width w of a rectangular region is 190 meters.Find the dimensions that produce the greatest area.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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15
The height in feet of a projectile with an initial velocity of 96 feet per second and an initial height of 75 feet is a function of time t, in seconds, given by Find the maximum height of the projectile.
A) 254 ft
B) 219 ft
C) 263 ft
D) 105 ft
E) 315 ft
Find the maximum height of the projectile.A) 254 ft
B) 219 ft
C) 263 ft
D) 105 ft
E) 315 ft
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16
The path of a diver is given by where is the height (in feet) and is the horizontal distance from the end of the diving board (in feet).Find the maximum height of the diver.
A) 12 feet
B) 13 feet
C) 10 feet
D) 14 feet
E) 17 feet
where is the height (in feet) and is the horizontal distance from the end of the diving board (in feet).Find the maximum height of the diver.A) 12 feet
B) 13 feet
C) 10 feet
D) 14 feet
E) 17 feet
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17
Compare the graph of with
A) shifts right units, shifts downward units, and shrinks by a factor of
B) shifts right units, shifts upward units, and stretches by a factor of
C) shifts left units, shifts downward units, and stretches by a factor of
D) shifts right units, shifts upward units, and shrinks by a factor of
E) shifts left units, shifts upward units, and stretches by a factor of
with A)
shifts right units, shifts downward units, and shrinks by a factor of B)
shifts right units, shifts upward units, and stretches by a factor of C)
shifts left units, shifts downward units, and stretches by a factor of D)
shifts right units, shifts upward units, and shrinks by a factor of E)
shifts left units, shifts upward units, and stretches by a factor of فتح الحزمة
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18
Examine the leading term and determine the far-left and far-right behavior of the graph of the polynomial function
A) down to the far left, up to the far right
B) down to the far left, down to the far right
C) up to the far left, up to the far right
D) up to the far left, down to the far right
E) cannot be determined
A) down to the far left, up to the far right
B) down to the far left, down to the far right
C) up to the far left, up to the far right
D) up to the far left, down to the far right
E) cannot be determined
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19
The fuel efficiency, in miles per gallon, for a certain midsize car at various speeds, in miles per hour, is given in the table below. Find a quadratic model for these data and use it to predict the fuel efficiency of this car when it is traveling at a speed of 40 mph.Do not round any values in your calculations but round the final answer to the nearest tenth.
A) 33.9 mpg
B) 33.7 mpg
C) 35.7 mpg
D) 32.7 mpg
E) 33.9 mpg
Find a quadratic model for these data and use it to predict the fuel efficiency of this car when it is traveling at a speed of 40 mph.Do not round any values in your calculations but round the final answer to the nearest tenth.A) 33.9 mpg
B) 33.7 mpg
C) 35.7 mpg
D) 32.7 mpg
E) 33.9 mpg
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20
Find an equation of the parabola below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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21
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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22
Write in the form when
A)
B)
C)
D)
E)
in the form when A)
B)
C)
D)
E)
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23
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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24
Use long division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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25
Use long division to divide the first polynomial below by the second.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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26
Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
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27
Find all the real zeros of the polynomial function and determine the multiplicity of each.
A) , multiplicity 2; , multiplicity 1
B) , multiplicity 1; , multiplicity 1; , multiplicity 1
C) , multiplicity 2; , multiplicity 1
D) , multiplicity 1; , multiplicity 1; , multiplicity 1
E) , multiplicity 3
and determine the multiplicity of each.A)
, multiplicity 2; , multiplicity 1B)
, multiplicity 1; , multiplicity 1; , multiplicity 1C)
, multiplicity 2; , multiplicity 1D)
, multiplicity 1; , multiplicity 1; , multiplicity 1E)
, multiplicity 3 فتح الحزمة
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28
Use synthetic division to divide by
A)
B)
C)
D)
E)
by A)
B)
C)
D)
E)
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29
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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30
Using the factors and , find the remaining factor(s) of and write the polynomial in fully factored form.
A)
B)
C)
D)
E)
and , find the remaining factor(s) of and write the polynomial in fully factored form.A)
B)
C)
D)
E)
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31
A closed box is to be constructed from a rectangular sheet of cardboard that measures 57 inches by 28 inches.The box is made by cutting rectangles that measure x inches by 2x inches from two of the corners and by cutting two squares that measure x inches by x inches from the top and from the bottom of the rectangle, as shown in the following figure.Use a graphing calculator to determine what value of x (to the nearest thousandth of an inch) will produce a box with maximum volume?
A) 5.314
B) 21.000
C) 4.222
D) 16.686
E) 3.707
A) 5.314
B) 21.000
C) 4.222
D) 16.686
E) 3.707
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32
Use synthetic division and the Factor Theorem to determine whether or not is a factor of
A) Yes, is a factor.
B) No, is not a factor.
is a factor of A) Yes,
is a factor.B) No,
is not a factor. فتح الحزمة
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33
Use synthetic division and the Factor Theorem to determine whether or not is a factor of
A) No, is not a factor.
B) Yes, is a factor.
is a factor of A) No,
is not a factor.B) Yes,
is a factor. فتح الحزمة
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34
Sketch the graph of the polynomial function Do not use a graphing calculator.
A)
B)
C)
D)
E)
Do not use a graphing calculator.A)
B)
C)
D)
E)
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35
Match the graph with one of the following functions below. Function I : Function II : Function III : Function IV : Function V :
A) Function I
B) Function IV
C) Function V
D) Function II
E) Function III
Function I : Function II : Function III : Function IV : Function V : A) Function I
B) Function IV
C) Function V
D) Function II
E) Function III
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36
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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37
Sketch the graph of the polynomial function below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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38
Use synthetic division to divide.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
فتح الحزمة
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39
Find the real zeros of the polynomial function and determine the multiplicity of each.
A) , multiplicity 2; , multiplicity 3
B) , multiplicity 2; , multiplicity 1; , multiplicity 2
C) , multiplicity 3; , multiplicity 2
D) , multiplicity 3; , multiplicity 2
E) , multiplicity 2; , multiplicity 2; , multiplicity 1
and determine the multiplicity of each.A)
, multiplicity 2; , multiplicity 3B)
, multiplicity 2; , multiplicity 1; , multiplicity 2C)
, multiplicity 3; , multiplicity 2D)
, multiplicity 3; , multiplicity 2E)
, multiplicity 2; , multiplicity 2; , multiplicity 1 فتح الحزمة
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40
If , use synthetic division to evaluate
A)
B)
C)
D)
E)
, use synthetic division to evaluate A)
B)
C)
D)
E)
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41
Simplify the rational expression, , by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
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42
Find all the rational zeros of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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43
Write the complex number in standard form.
A)
B)
C)
D)
E)
in standard form.A)
B)
C)
D)
E)
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44
Find the zeros of the polynomial function below.If a zero is a multiple zero, state its multiplicity.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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45
Find all real solutions of the polynomial equation
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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46
Use the Rational Zero Test to list all possible rational zeros of the polynomial function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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47
Simplify the rational expression, , by using long division or synthetic division.
A)
B)
C)
D)
E)
, by using long division or synthetic division.A)
B)
C)
D)
E)
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48
Find all the real zeros of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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49
Find all real solutions of the polynomial equation
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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50
A farmer wants to enlarge an existing rectangular pig pen such that the total area of the new pen is twice as large as the original pen.The current pen's dimensions are 25' × 27'.The farmer wants to add 13 feet more to the long side than to the the short side.Find the dimensions of the new pen.
A) 5 feet × 18 feet
B) 30 feet × 45 feet
C) 30 feet × 32 feet
D) 30 feet × 43 feet
E) 30 feet × 40 feet
A) 5 feet × 18 feet
B) 30 feet × 45 feet
C) 30 feet × 32 feet
D) 30 feet × 43 feet
E) 30 feet × 40 feet
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51
An open box is to be made from a square piece of cardboard, 72 inches on a side, by cutting equal squares with sides of length x from the corners and turning up the sides (see figure below).After determining the function V, in terms of x, that represents the volume of the box, use a graphing utility to estimate the dimensions that will maximize its volume.
A) × ×
B) × ×
C) × ×
D) × ×
E) × ×
A)
× × B)
× × C)
× × D)
× × E)
× × فتح الحزمة
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52
Find all the rational zeros of the function
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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53
Write the complex number in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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54
Evaluate the power of i.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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55
The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height. If the volume of the box is 440 cubic inches, find the dimensions of the box.
A) 5 in. by 11 in. by 8 in.
B) 4 in. by 9 in. by 7 in.
C) 109 in. by 219 in. by 112 in.
D) 5.5 in. by 12 in. by 8.5 in.
E) 106 in. by 213 in. by 109 in.
A) 5 in. by 11 in. by 8 in.
B) 4 in. by 9 in. by 7 in.
C) 109 in. by 219 in. by 112 in.
D) 5.5 in. by 12 in. by 8.5 in.
E) 106 in. by 213 in. by 109 in.
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56
Find real numbers a and b such that the equation is true.
A)
B)
C)
D)
E)
is true.A)
B)
C)
D)
E)
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57
Use the zero or root feature of a graphing utility to approximate the real zeros of the function accurate to the nearest thousandth.
A) , 1.732, 1.414
B) -1.732, -1.414
C) 1.732, 1.414
D) 1.732, 1.414
E) , - 1.732, 1.414
accurate to the nearest thousandth.A)
, 1.732, 1.414B) -1.732, -1.414
C)
1.732, 1.414D) 1.732, 1.414
E)
, - 1.732, 1.414 فتح الحزمة
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58
Use the Rational Zero Test to list possible rational zeros for the polynomial function below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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59
Find all the real zeros of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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60
A company that produces video games estimates that the profit (in dollars) for selling a new game is given by where is the advertising expense (in tens of thousands of dollars).Using this model, how much should the company spend on advertising to obtain a profit of $6,500,000? Round to the nearest dollar.
A) $399,893 or $744,397
B) $433,844 or $721,190
C) $315,902 or $794,255
D) $368,914 or $764,017
E) $344,417 or $778,509
(in dollars) for selling a new game is given by where is the advertising expense (in tens of thousands of dollars).Using this model, how much should the company spend on advertising to obtain a profit of $6,500,000? Round to the nearest dollar.A) $399,893 or $744,397
B) $433,844 or $721,190
C) $315,902 or $794,255
D) $368,914 or $764,017
E) $344,417 or $778,509
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61
Simplify and write the following complex number in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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62
Combine and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
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63
Simplify and write the following complex number in standard form.
A)
B)
C)
D)
E) 0
A)
B)
C)
D)
E) 0
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64
Use the quadratic formula to solve
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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65
Write the polynomial as the product of factors that are irreducible over the rationals.
A)
B)
C)
D)
E)
as the product of factors that are irreducible over the rationals.A)
B)
C)
D)
E)
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66
Simplify and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
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67
Simplify and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
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68
Simplify and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
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69
Classify whether the following numbers are in the Mandelbrot Set. I : II : III :
A) Only numbers I and III are in the Mandelbrot Set.
B) Only number II is in the Mandelbrot Set.
C) Only number I is in the Mandelbrot Set.
D) None are in the Mandelbrot Set.
E) Only numbers II and III are in the Mandelbrot Set.
II : III : A) Only numbers I and III are in the Mandelbrot Set.
B) Only number II is in the Mandelbrot Set.
C) Only number I is in the Mandelbrot Set.
D) None are in the Mandelbrot Set.
E) Only numbers II and III are in the Mandelbrot Set.
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70
Write the following expression as a complex number in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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71
Simplify and write the following complex number in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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72
Simplify and write the answer in standard form.
A)
B)
C)
D)
E)
and write the answer in standard form.A)
B)
C)
D)
E)
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73
Write as a product of linear factors given that and are zeros of the polynomial.
A)
B)
C)
D)
E)
as a product of linear factors given that and are zeros of the polynomial.A)
B)
C)
D)
E)
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74
Find all the zeros of the polynomial function and write the polynomial as a product of its linear factors.
A) , , ;
B) , , ;
C) , , ;
D) , , ;
E) , , ;
and write the polynomial as a product of its linear factors.A)
, , ; B)
, , ; C)
, , ; D)
, , ; E)
, , ; فتح الحزمة
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75
Plot the complex number below.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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76
The demand and cost equations for a stethoscope are given by and where is the unit price (in dollars), is the total cost (in dollars), and is the number of units.The total profit (in dollars) obtained by producing and selling units is given by Determine a price that would yield a profit of $4 million.
A) $22.21
B) $44.43
C) $88.85
D) $99.96
E) $66.64
and where is the unit price (in dollars), is the total cost (in dollars), and is the number of units.The total profit (in dollars) obtained by producing and selling units is given by Determine a price that would yield a profit of $4 million.A) $22.21
B) $44.43
C) $88.85
D) $99.96
E) $66.64
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77
Determine the number of zeros of the polynomial function below.
A) 1
B) 3
C) 4
D) 5
E) 6
A) 1
B) 3
C) 4
D) 5
E) 6
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78
Write as a product of linear factors.
A)
B)
C)
D)
E)
as a product of linear factors.A)
B)
C)
D)
E)
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79
Write as a product of linear factors given that and are zeros of the polynomial.
A)
B)
C)
D)
E)
as a product of linear factors given that and are zeros of the polynomial.A)
B)
C)
D)
E)
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80
Simplify and write the following complex number in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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