Deck 3: Functions and Graphs

Question 1

The population $y$ (in millions of people) of North America from 1980 to 2050 can be modeled by $y = 5.3 x + 430,$ $- 30 \leq x \leq 40$ where $x$ represents the year, with $x = 40$ corresponding to 2050. Find the y-intercept of the graph of the model. What does it represent in the given situation?

A) $( 0,483 );$ It represents the population (in millions of people)of North America in 2020.
B) $( 0,536 );$ It represents the population (in millions of people)of North America in 2030.
C) $( 0,377 );$ It represents the population (in millions of people)of North America in 2000.
D) $( 0,430 );$ It represents the population (in millions of people)of North America in 2010.
E) $( 0,324 );$ It represents the population (in millions of people)of North America in 1990.

Answer 1

$( 0,430 );$ It represents the population (in millions of people)of North America in 2010.

Question 2

Find an equation of a circle that satisfies the following condition. Write your answer in standard form. Center: $( 1,2 )$ ; passing through $( 5 , - 3 )$

A) $( x + 1 ) ^ { 2 } + ( y + 2 ) ^ { 2 } = ( \sqrt { 41 } ) ^ { 2 }$
B) $( x - 5 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = ( \sqrt { 41 } ) ^ { 2 }$
C) $( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = ( \sqrt { 34 } ) ^ { 2 }$
D) $( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = ( \sqrt { 41 } ) ^ { 2 }$
E) $( x - 5 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = ( \sqrt { 34 } ) ^ { 2 }$

Answer 2

$( x - 1 ) ^ { 2 } + ( y - 2 ) ^ { 2 } = ( \sqrt { 41 } ) ^ { 2 }$

Question 3

Find the midpoint of the line segment joining the points. (0, 9), (4, -3)

A)(-2, -3)
B)(3, 2)
C)(6, -2)
D)(-2, 6)
E)(2, 3)

Answer 3

(2, 3)

Question 4

Assuming that the graph shown has y-axis symmetry, sketch the complete graph.

A)
B)
C)
D)
E)

Question 5

Find the x- and y-intercepts of the graph of the equation below. $y = x \sqrt { x + 3 }$

A) $( 3,0 ) , ( 0,3 )$
B) $( 0,0 ) , ( - 3,0 )$
C) $( 0,0 ) , ( 3,0 )$
D) $( 0,0 ) , ( - 3,0 ) , ( 3,0 )$
E) $( 0,0 ) , ( 3,0 ) , ( 0,3 )$

Question 6

Write the standard form of the equation of the circle whose diameter has endpoints of $( 8 , - 12 )$ and $( 14 , - 4 )$ .

A) $( x - 11 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 25$
B) $( x - 11 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 5$
C) $( x + 8 ) ^ { 2 } + ( y - 11 ) ^ { 2 } = 25$
D) $( x - 8 ) ^ { 2 } + ( y + 11 ) ^ { 2 } = 25$
E) $( x + 11 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 5$

Question 7

Estimate the slope of the line.

A) $- \frac { 1 } { 2 }$
B) $2$
C) $- 2$
D) $\frac { 1 } { 2 }$
E) $- 3$

Question 8

Match the equation below with its graph. $y = 4 + x$ Graph I : Graph IV : Graph II : Graph V : Graph III :

A)Graph IV
B)Graph III
C)Graph V
D)Graph II
E)Graph I

Question 9

Sketch the graph of the equation below. $y = \sqrt { x + 1 }$

A)
B)
C)
D)
E)

Question 10

Find the x- and y-intercepts of the graph of the following equation. $9 x + 6 y = 11$

A)x-int: $\left( \frac { 3 } { 2 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 2 } { 3 } \right)$
B)x-int: $\left( \frac { 3 } { 2 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 11 } { 6 } \right)$
C)x-int: $\left( \frac { 11 } { 9 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 11 } { 6 } \right)$
D)x-int: $\left( \frac { 9 } { 11 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 3 } { 2 } \right)$
E)x-int: $\left( \frac { 11 } { 9 } , 0 \right)$ ; y-int: $\left( 0 , \frac { 2 } { 3 } \right)$

Question 11

Plot the points and find the slope of the line passing through the pair of points. (0, 4), (5, 2)

A)slope: $- \frac { 5 } { 2 }$
B)slope: $\frac { 5 } { 2 }$
C)slope: $- \frac { 4 } { 3 }$
D)slope: $- \frac { 2 } { 5 }$
E)slope: $\frac { 2 } { 5 }$

Question 12

Find the slope of the line that passes through the points $( 7 , - 2 )$ and $( 7 , - 3 ).$

A)-9
B)-1
C)1
D)0
E)undefined

Question 13

Find the distance between the points. Round to the nearest hundredth, if necessary. (-6, 2), (7, -4)

A)2.24
B)6.08
C)14.32
D)13.15
E)13.6

Question 14

Given $x ^ { 2 } + y ^ { 2 } = 4$ , use the algebraic tests to determine symmetry with respect to both axes and the origin.

A)y-axis symmetry only
B)x-axis symmetry only
C)origin symmetry only
D)x-axis, y-axis, and origin symmetry
E)no symmetry

Question 15

Find $x$ such that the distance between the point $( - 2,5 )$ and $( x , 17 )$ is 15.

A) $x = - 14 , - 11$
B) $x = - 14,10$
C) $x = - 11,10$
D) $x = - 14,7$
E) $x = - 11,7$

Question 16

Plot the points below whose coordinates are given on a Cartesian coordinate system. $( 0,8 ) , ( - 8,5 ) , ( - 2 , - 2 ) , ( 5,0 )$

A)
B)
C)
D)
E)

Question 17

Sketch the graph of the equation below. $x ^ { 2 } + y ^ { 2 } = 9$

A)
B)
C)
D)
E)

Question 18

Graph the following equation by plotting points that satisfy the equation. $y = | x + 1 | - 2$

A)
B)
C)
D)
E)

Question 19

After completing the table, use the resulting solution points to sketch the graph of the equation .

Question 20

Given $y = \frac { x ^ { 3 } } { x ^ { 4 } + 1 }$ , use the algebraic tests to determine symmetry with respect to both axes and the origin.

A)y-axis symmetry only
B)x-axis symmetry only
C)origin symmetry only
D)x-axis, y-axis, and origin symmetry
E)no symmetry

Question 21

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (-5, -9), (-7, 2)
L2 : (-8, 1), (-19, -1)

A)parallel
B)perpendicular
C)neither

Question 22

Suppose the average remaining lifetime for women in a given country is given in the following table. $$\begin{array} { | c | c | } \hline \text { Age } & \text { Years } \\\hline 5 & 75.2 \\\hline 30 & 54.3 \\\hline 50 & 37.5 \\\hline 65 & 25.4 \\\hline 75 & 17.0 \\\hline\end{array}$$ Compute the linear regression equation for these data, where x is the age, in years, and A is the remaining lifetime, in years. Round parameters to the nearest hundredth.

A) $A ( x ) = - 14.53 x + 44.37$
B) $A ( x ) = - 0.83 x + 44.37$
C) $A ( x ) = - 14.53 x + 85.47$
D) $A ( x ) = - 14.53 x + 79.27$
E) $A ( x ) = - 0.83 x + 79.27$

Question 23

Use the point on the line and the slope of the line to determine whether any of the three additional points lies on the line. Point $~~~~~~~~~~~~~$ Slope
$( - 2,4 )~~~~~~~~$$m = \frac { 1 } { 2 }$ I: $\quad ( 8,6 )$
II: $\quad ( 2,6 )$
III: $\quad ( 4,7 )$

A)Only points II and III lie on the line.
B)Only point II lies on the line.
C)Only point III lies on the line.
D)Only points I and II lie on the line.
E)Only points I and III lie on the line.

Question 24

Use the intercept form to find the equation of the line with the given intercepts. The intercept form of the equation of a line with intercepts (a, 0) and (0, b) is $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$
$x$ -intercept: $( - 4,0 ) \quad y$ -intercept: $( 0,1 )$

A)x - 4y = 1
B) $x - 4 y = - \frac { 1 } { 4 }$
C) $- 4 x + y = - \frac { 1 } { 4 }$
D)4x - y = 4
E)x - 4y = -4

Question 25

Write the equation that expresses the relationship between the variables described below, then use the given data to solve for the variation of constant. "y varies directly as $z$ , and $y = 86.66$ when $z = 14.$ "

A) $y = \frac { k } { z }$ ; $k = 1213.24$
B) $y = \sqrt { k } z$ ; $k = 38.32$
C) $y = k z$ ; $k = 6.19$
D) $y = k ^ { 2 } z$ ; $k = 2.49$
E) $y = \sqrt { k z }$ ; $k = 536.43$

Question 26

Find the slope and y-intercept of the equation of the line. -3y - 9x = -12

A)slope: 9; y-intercept: -12
B)slope: -12; y-intercept: 9
C)slope: 9; y-intercept: -3
D)slope: 4; y-intercept: -3
E)slope: -3; y-intercept: 4

Question 27

Find the slope and y-intercept of the equation of the line. $y = 3 x - 4$

A)slope: $\frac { 1 } { 3 }$ ; y-intercept: -4
B)slope: $- \frac { 1 } { 4 }$ ; y-intercept: 3
C)slope: 3; y-intercept: -4
D)slope: -4; y-intercept: 3
E)slope: 3; y-intercept: 4

Question 28

Assume that y is directly proportional to x. If $x = 36$ and $y = 27$ , determine a linear model that relates y and x.

A) $y = \frac { 4 } { 3 } x$
B) $y = \frac { 3 } { 5 } x$
C) $y = \frac { 3 } { 2 } x$
D) $y = \frac { 3 } { 4 } x$
E) $y = \frac { 2 } { 3 } x$

Question 29

After opening the parachute, the descent of a parachutist follows a linear model. At 3:31 P.M., the height of the parachutist is 2800 feet. At 3:32 P.M., the height is 1600 feet. Use a linear equation that gives the height of the parachutist in terms of the time to find the time when the parachutist will reach the ground.

A)3:33:40 P.M.
B)3:33:20 P.M.
C)3:32:10 P.M.
D)3:34:00 P.M.
E)3:33:50 P.M.

Question 30

Find the slope of the line that passes through the points $A ( - 4 , - 2 ) \text { and } B ( 10,9 ).$

A) $\frac { 11 } { 14 }$
B) $- \frac { 1 } { 2 }$
C) $- \frac { 11 } { 14 }$
D) $\frac { 13 } { 12 }$
E) $\frac { 7 } { 6 }$

Question 31

Which of the following graphs below can be approximated by a linear model? I II III

A)None can be modeled linearly.
B)Only graph III can be modeled linearly.
C)Only graphs I and II can be modeled linearly.
D)Only graphs I and III can be modeled linearly.
E)Graphs I, II, and III can be modeled linearly.

Question 32

A car was purchased for $42,000. Assuming the car depreciates at a rate of $5040 per year (straight-line depreciation) for the first 5 years, write the value v of the car as a function of the time t (measured in years) for $0 \leq t \leq 5$

A) $v ( t ) = 5040 t - 42,000$
B) $v ( t ) = 42,000 - 5040 ( 5 ) t$
C) $v ( t ) = 42,000 - 5040 t$
D) $v ( t ) = 42,000 + 5040 ( 5 ) t$
E) $v ( t ) = 42,000 + 5040 t$

Question 33

The sales tax on an item with a retail price of $612 is $61.20. Create a mathematical model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $70.38.

A) $\$ 716.03$
B) $\$ 705.79$
C) $\$ 648.11$
D) $\$ 675.43$
E) $\$ 703.80$

Question 34

The simple interest on an investment is directly proportional to the amount of the investment. By investing $8750 in a certain certificate of deposit, you obtained an interest payment of $210.00 after 1 year. Determine a mathematical model that gives the interest, I, for this CD after 1 year in terms of the amount invested, P.

A) $I = ( 0.022 ) P$
B) $I = ( 0.027 ) P$
C) $I = ( 0.019 ) P$
D) $I = ( 0.028 ) P$
E) $I = ( 0.024 ) P$

Question 35

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (-8, 0), (4, -3)
L2 : (0, 1), (-4, 2)

A)parallel
B)perpendicular
C)neither

Question 36

Graph y as a function of x by finding the slope and y-intercept of the line below. $y = 3 x + 1$

A)
B)
C)
D)
E)

Question 37

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (1, 9), (-4, 8)
L2 : (8, -7), (7, -1)

A)parallel
B)perpendicular
C)neither

Question 38

Determine if lines $L _ { 1 }$ and $L _ { 2 }$ are parallel, perpendicular, or neither. $L _ { 1 } : 4 x - 4 y = - 4$ $L _ { 2 } : 8 x + 8 y = 9$

A)parallel
B)neither
C)perpendicular

Question 39

The table below shows the velocities, in feet per second, of a ball that is thrown horizontally from the top of a 50 foot building and the distances, in feet, that it lands from the base of the building. Compute the linear regression equation for these data. $\begin{array} { c c } \text { Velocity } ( \mathrm { ft } / \mathrm { sec } ) & \text { Distance } ( \mathrm { ft } ) \\15 & 48 \\25 & 80 \\29 & 100 \\33 & 95 \\38 & 112 \\40 & 130 \\48 & 150\end{array}$

A) $y = 3.02463355 x + 3.626221498$
B) $y = 3.156886228 x + .5988023952$
C) $y = 3.073502956 x + 2.338987407$
D) $y = 3.028222013 x - 1.079962371$
E) $y = 2.944432432 x - 0.7139459459$

Question 40

Plot the points and find the slope of the line passing through the pair of points. (1, 0), (-2, 0)

A)slope: 0
B)slope: 1
C)slope: -3
D)slope: $- \frac { 1 } { 3 }$
E)slope: undefined

Question 41

The marketing department of a company estimates that the demand for a product is given by $p = 180 - 0.0001 x,$ where $p$ is the price per unit and $x$ is the number of units. The cost $C$ of producing $x$ units is given by $C = 450,000 + 50 x,$ and the profit $P$ for producing and selling $x$ units is given by $P = R - C = x p - C.$ Sketch the graph of the profit function and estimate the number of units that would produce a maximum profit.

A)690,000 units
B)650,000 units
C)610,000 units
D)710,000 units
E)580,000 units

Question 42

Sketch the graph of the function below. $f ( x ) = \sqrt { - x + 3 }$

A)
B)
C)
D)
E)

Question 43

Which set of ordered pairs represents a function from P to Q? P = {5, 10, 15, 20} Q = {-2, 0, 2}

A){(5, -2), (10, 0), (10, 2), (15, 0), (20, -2)}
B){(15, -2), (15, 0), (15, 2)}
C){(15, 0), (10, -2), (5, 0), (10, 2), (15, -2)}
D){(10, 0), (15, 2), (20, 0)}
E){(5, 2), (15, 0), (5, -2), (15, 2)}

Question 44

Find all real values of x such that f (x) = 0. $f ( x ) = 4 x ^ { 2 } - 25$

A) $\pm \frac { 2 } { 5 }$
B) $\pm \frac { 5 } { 2 }$
C) $\pm \frac { 25 } { 4 }$
D) $- \frac { 25 } { 4 }$
E) $\frac { 5 } { 2 }$

Question 45

The national defense budget expenses $V$ (in billions of dollars) for veterans in the United States from 1990 to 2005 can be approximated by the model $$V = \left\{ \begin{array} { c c } - 0.326 t ^ { 2 } + 3.40 t + 28.7 , & 0 \leq t \leq 6 \\0.441 t ^ { 2 } - 6.23 t + 62.6 , & 7 \leq t \leq 15\end{array} \right.$$ where $t$ represents the year, with $t = 0$ corresponding to 1990. Use the model to find total veteran expenses in 1995.

A)$61.816 billion
B)$37.550 billion
C)$37.364 billion
D)$32.894 billion
E)$44.736 billion

Question 46

Use the graph of the function to find the domain and range of f.

A) domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range : $( - \infty , - 2 ) \cup ( - 1 , \infty )$
B) $\begin{array} { l } \text { domain : } ( - \infty , - 2 ) \cup ( - 2 , \infty ) \\\text { range : } ( - 1,1 )\end{array}$
C) $\begin{array} { l } \text { domain : } ( - \infty , - 2 ) \cup ( - 2 , \infty ) \\\text { range : } \{ - 2 , - 1 \}\end{array}$
D) domain : all real numbers
range: $( - 1,1 )$
E) domain : $\{ - 2 , - 1 \}$
range : $( - \infty , - 2 ) \cup ( - 2 , \infty )$

Question 47

Find the domain of the function. $f ( y ) = \frac { - 6 y } { y + 9 }$

A)all real numbers $y \neq - 9$
B)all real numbers $y \neq - 9$ , $y \neq 0$
C)all real numbers
D)y = -9, y = 0
E)y = -9

Question 48

Use a graphing utility to graph the function and approximate (to two decimal places) any relative minimum or relative maximum values. f (x) = x3 - x2 - 2x - 1

A)relative maximum: (-0.55, -0.37)relative minimum: (1.22, -3.11)
B)relative maximum: (1.22, -3.11)relative minimum: (-0.55, -0.37)
C)relative maximum: (-0.37, -0.55)relative minimum: (-3.11, 1.22)
D)relative maximum: (-3.11, 1.22)relative minimum: (-0.37, -0.55)
E)relative maximum: (-3.11, -34.62)relative minimum: (-0.37, -0.45)

Question 49

The inventor of a new game believes that the variable cost of producing the game is $3.75 per unit and the fixed costs are $5000. The inventor sells each game for $8.99. Let $x$ be the number of games sold. Write the average cost per unit $\bar { C } = C / x$ as a function of $x$ where $C$ is defined as the total cost of producing $x$ games.

A) $\bar { C } = \frac { 5000 } { x } - 5.24 x$
B) $\bar { C } = 5000 + 3.75 x$
C) $\bar { C } = 5000 - 5.24 x$
D) $\bar { C } = \frac { 5000 } { x } + 3.75$
E) $\bar { C } = \frac { 5000 } { x } - 5.24$

Question 50

Find all real values of x such that f (x) = 0. $f ( x ) = \frac { 7 x - 4 } { 5 }$

A) $\frac { 4 } { 35 }$
B) $\pm \frac { 4 } { 35 }$
C) $\pm \frac { 4 } { 7 }$
D) $\frac { 4 } { 7 }$
E) $- \frac { 4 } { 7 }$

Question 51

Suppose the average remaining lifetime for women in a given country is given in the following table. $$\begin{array} { | c | c | } \hline \text { Age } & \text { Years } \\\hline 5 & 72.4 \\\hline 25 & 53.1 \\\hline 30 & 49.5 \\\hline 35 & 44.5 \\\hline 40 & 39.2 \\\hline\end{array}$$ Find the linear regression equation for these data, whose parameters are rounded to the nearest hundredth, where x is the age, in years, and A is the remaining lifetime, in years. Use the regression equation to estimate the remaining lifetime for a 31-year old woman.

A)42.29 years
B)50.75 years
C)46.99 years
D)55.45 years
E)52.63 years

Question 52

An open box is to be made from a square piece of cardboard having dimensions 22 inches by 22 inches by cutting out squares of area $x ^ { 2 }$ from each corner as shown in the figure below. If the volume of the box is given by $V ( x ) = 484 x - 88 x ^ { 2 } + 4 x ^ { 3 },$ state the domain of V . $$22 - 2 x$$ $$22 - 2 x$$

A) $0 < x < 22$
B) $0 < x < 11$
C) $88 < x < 484$
D) $4 < x < 88$
E)all real numbers

Question 53

Use the vertical line test to determine if the following graph is the graph of a function.

A)function
B)not a function

Question 54

Given $t ( x ) = 3 x ^ { 2 } + 5,$ find $t ( - 8 ).$

A)192
B)-19
C)187
D)-43
E)197

Question 55

Which graph represents the function? $g ( x ) = \llbracket 2 x \rrbracket$

A)
B)
C)
D)
E)

Question 56

An open box is to be made from a square piece of cardboard having dimensions 32 inches by 32 inches by cutting out squares of area $x ^ { 2 }$ from each corner as shown in the figure below. Express the volume V of the box as a function of x. $$32 - 2 x$$ $$32 - 2 x$$

A) $V ( x ) = 32 x ^ { 2 } - 2 x ^ { 3 }$
B) $V ( x ) = 32 x - 64 x ^ { 2 } + 4 x ^ { 3 }$
C) $V ( x ) = 1024 - 128 x + 4 x ^ { 2 }$
D) $V ( x ) = 1024 x - 128 x ^ { 2 } + 4 x ^ { 3 }$
E) $V ( x ) = 1024 x - 64 x ^ { 2 } + 4 x ^ { 3 }$

Question 57

Given $m ( x ) = 3 x ^ { 2 } - 6,$ find $m ( r ).$

A) $3 r ^ { 2 } - 6$
B) $9 r ^ { 2 } + 36$
C) $- 3 r ^ { 2 }$
D) $9 r ^ { 2 } - 6$
E) $3 r ^ { 2 } - 6 r$

Question 58

Given $q ( x ) = 6 x ^ { 2 } - 3,$ find $q ( 3 ).$

A)33
B)15
C)51
D)54
E)57

Question 59

Find the domain of the function. $q ( w ) = \sqrt { 1 - w ^ { 2 } }$

A)-1 $\le$ w $\le$ 1
B)w $\le$ -1 or w $\ge$ 1
C)w $\ge$ 0
D)w $\le$ 1
E)all real numbers

Question 60

Evaluate the function at the specified value of the independent variable and simplify. g (s) = -6s + 3; g (-0.2)

A)1.2s - 18
B)-1.8
C)4.2
D)-0.2s + 3
E)-0.2s - 3

Question 61

Use the graph of $f ( x ) = | x |$ to write an equation for the function whose graph is shown.

A) $f ( x ) = | - 3 x - 1 | + 2$
B) $f ( x ) = | - 3 x + 1 | + 2$
C) $f ( x ) = - 3 | x + 1 | - 2$
D) $f ( x ) = - 3 | x - 1 | + 2$
E) $f ( x ) = - 3 | x + 1 | + 2$

Question 62

Use a graphing utility to graph the function, approximate the relative minimum or maximum of the function, and estimate the open intervals on which the function is increasing or decreasing. $f ( x ) = x ^ { 2 } - 4 x + 1$

A) Decreasing on $( - \infty , 2 )$ Increasing on $( 2 , \infty )$ Relative minimum: $( 2 , - 3 )$
B) Decreasing on $( 3 , \infty )$ Increasing on $( - \infty , 3 )$ Relative maximum: $( 3,12 )$
C) Decreasing on $( 0,2 )$ Increasing on $( - \infty , 0 ) , ( 2 , \infty )$ Relative minimum: $( 0,0 )$ Relative maximum: $( 2 , - 4 )$
D) Decreasing on $( - \infty , - 1 ) , ( 1 , \infty )$ Increasing on $( - 1,1 )$ Relative minimum: $( - 1 , - 1 )$ Relative maximum: $( 1,3 )$
E) Decreasing on $( 1 , \infty )$ Increasing on $( - \infty , 1 )$ Relative minimum: $( - 1,1 )$ Relative maximum: $( 1,2 )$

Question 63

The cost of sending an overnight package from New York to Atlanta is $9.80 for up to, but not including, the first pound and $3.50 for each additional pound (or portion of a pound). A model for the total cost $C$ of sending the package is $C = 9.80 + 3.50$$\lfloor x \rfloor,$ $x > 0,$ where $x$ is the weight of the package (in pounds). Sketch the graph of this function. Note that the function $\lfloor x \rfloor$ is the greatest integer function.

A)
B)
C)
D)
E)

Question 64

Use the graph of $f ( x ) = x ^ { 3 }$ to write equations for the functions whose graphs are shown.

A) $y = - x ^ { 3 }$
B) $( x + 1 ) ^ { 3 } + 1$
C) $x ^ { 2 }$
D) $x ^ { 2 } + 1$
E) $- x ^ { 2 } + 1$

Question 65

Describe the sequence of transformation from $f ( x ) = x ^ { 2 }$ to $g ( x )$ if $g ( x ) = ( x - 6 ) ^ { 2 } - 7$

A)Shifted seven units to the right and six units upwards.
B)Shifted seven units to the left and six units upwards.
C)Shifted six units to the right and seven units upwards.
D)Shifted six units to the left and seven units upwards.
E)Shifted six units to the right and seven units downwards.

Question 66

Describe the sequence of transformations from $f ( x ) = \sqrt { x }$ to $g$ . Then sketch the graph of $g$ by hand. Verify with a graphing utility. $g ( x ) = \sqrt { x - 3 }$

A)Shifted 5 units downward
B)Shifted 1 unit upward
C)Shifted 4 units to the left
D)Shifts 3 units to the right
E)4 units to the left and 2 units upward

Question 67

Consider the graph of $g ( x ) = \sqrt { x }.$ Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of $g$ is reflected in the x-axis, shifted eight units to the right, and shifted nine unit downward.

A) $h ( x ) = - \sqrt { x + 8 } - 9$
B) $h ( x ) = - \sqrt { x - 8 } - 9$
C) $h ( x ) = \sqrt { x - 8 } - 9$
D) $h ( x ) = \sqrt { x + 8 } + 9$
E) $h ( x ) = - \sqrt { x - 9 } + 8$

Question 68

Describe the sequence of transformations from $f ( x ) = | x |$ to $g$ . Then sketch the graph of $g$ by hand. Verify with a graphing utility. $f ( x ) = | x | + 2$

A)Vertical shifts down 3 units
B)Vertical shifts 2 units upward
C)Horizontal shift 1 unit to the right
D)Horizontal shifts 4 units to the left
E)Vertical shifts 3 units upward

Question 69

Use the graph of $$f$$ to sketch the graph of $y = f ( x ) + 2$ .

A)Horizontal shift 2 units to the right
B)Reflection in the x-axis
C)Vertical shift 2 units upward
D)Horizontal shift 3 units to the left
E)Stretching by 2

Question 70

Use the graph of $f ( x ) = x ^ { 2 }$ to write an equation for the function whose graphs is shown below.

A) $g ( x ) = ( x - 4 ) ^ { 2 }$
B) $g ( x ) = - ( x + 4 ) ^ { 2 }$
C) $g ( x ) = ( x + 2 ) ^ { 2 }$
D) $g ( x ) = - ( x - 2 ) ^ { 2 }$
E) $g ( x ) = - ( x - 4 ) ^ { 2 }$

Question 71

Consider the graph of $f ( x ) = x ^ { 3 }.$ Use your knowledge of rigid and nonrigid transformations to write an equation for the following descriptions. The graph of $f$ is shifted four units to the right.

A) $y = ( x + 4 ) ^ { 3 }$
B) $y = ( x - 4 ) ^ { 3 }$
C) $y = x ^ { 3 } - 4$
D) $y = x ^ { 3 } + 4$
E) $y = - 4 x ^ { 3 }$

Question 72

Use a graphing utility to graph the function and determine whether the function is even, odd, or neither. $f ( x ) = x ^ { 2 } - x ^ { 4 }$

A)Neither even nor odd
B)Odd
C)Even
D)Neither even nor odd
E)Even

Question 73

The weekly profit $P$ (in hundreds of dollars) for a business from a product is given by the model $P ( x ) = 70 - 20 x + 0.8 x ^ { 2 },$ $0 \leq x \leq 20$ where $x$ is the amount (in hundreds of dollars) spent on advertising. Rewrite the profit equation so that $x$ measures advertising expenditures in dollars.

A) $P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.8 x ^ { 2 }$
B) $P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.00008 x ^ { 2 }$
C) $P \left( \frac { x } { 100 } \right) = \frac { 7 } { 10 } - \frac { x } { 5 } + 0.008 x ^ { 2 }$
D) $P \left( \frac { x } { 100 } \right) = 70 - \frac { x } { 5 } + 0.00008 x ^ { 2 }$
E) $P \left( \frac { x } { 100 } \right) = 70 - \frac { x } { 5 } + 0.008 x ^ { 2 }$

Question 74

Decide whether the function is even, odd, or neither. $g ( x ) = x ^ { 3 } - 5 x$

A)Odd
B)Even
C)Neither even nor odd

Question 75

Describe the increasing, decreasing, and constant behavior of the function. Find the point or points where the behavior of the function changes. $f ( x ) = 2 x$

A)Increasing on $( - \infty , \infty )$ No change in the graph's behaviour
B)Decreasing on $( - \infty , 1 )$ Incresing on $( 1 , \infty )$ The graph's behaviour changes at the point $( 1 , - 1 )$
C)Increasing on $( - \infty , 0 )$ and $( 2 , \infty )$ Decresing on $( 0,2 )$ The graph's behaviour changes at the points $( 0,0 )$ and $( 2 , - 4 )$
D)Decreasing on $( - \infty , - 2 )$ Increasing on $( 2 , \infty )$ The graph's behaviour changes at the points $( - 2,0 )$ and $( 2,0 )$
E)Decreasing on $( - \infty , 0 )$ Incresing on $( 0 , \infty )$ The graph's behaviour changes at the point $( 0,0 )$

Question 76

Use the graph of $f ( x ) = x ^ { 3 } - 3 x ^ { 2 }$ to write an equation for the function $g$ .

A)The graph is shifted 2 units upward, so $g ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 2$
B)The graph is reflected in the x-axis and shifted 1 unit upward, so $g ( x ) = - x ^ { 3 } + 3 x ^ { 2 } + 1$
C)The graph is shifted 1 unit to the left,so $g ( x ) = x ^ { 3 } - 3 x - 2$
D)The graph is shifted 2 unit to the left, so $g ( x ) = - x ^ { 3 } + 3 x ^ { 2 } + 3 x + 2$
E)The graph is shifted 1 unit to the right $g ( x ) = x ^ { 3 } + 3 x + 1$

Question 77

Identify the transformation shown in the graph and identify the associated common function. Write the equation of the graphed function.

A)Common function: $y = x ^ { 3 }$ Transformation: horizontal shift 2 units to the rightEquation: $y = ( x - 2 ) ^ { 3 }$
B)Common function: $y = x$ Transformation: multiplied by $\frac { 1 } { 2 }$ shrinkingEquation: $y = \frac { 1 } { 2 } x$
C)Common function: $y = x ^ { 2 }$ Transformation: reflection about the x-axisEquation: $y = - x ^ { 2 }$
D)Common function: $y = c$ Transformation: $c$ is 7.Equation: $y = 7$
E)Common function: $y = \sqrt { x }$ Transformation: reflection about the x-axis and a vertical shift 1 unit upwardEquation: $y = - \sqrt { x } + 1$

Question 78

Sketch the graph of the function. $f ( x ) = x ^ { 2 } - 9$

A)
B)
C)
D)
E)

Question 79

Evaluate the function at each specified value of the independent variable. $f ( x ) =$ a) $f ( 2 )$ b) $f ( 2.5 )$ c) $f ( - 2.5 )$ d) $f ( - 4 )$

A)2, 2, -3, -4
B)2, 3, -3, -4
C)2, 2, -2, -4
D)2, 2.5, 2.5, 4
E)2, 2.5, -2.5, -4

Question 80

Sketch the graph of the function. $f ( x ) =$

A)
B)
C)
D)
E)