Question 1

Determine whether the relation represents a function. If it is a function, state the domain and range.&#10;{(-4, 19), (-3, 12), (0, 3), (3, 12), (5, 28)}&#10;A)  &#10;B)  &#10;C) not a function

Accepted Answer

11ebb6d7_48d9_d090_b437_738b2b047dc0_TB8593_11

Question 2

The graph of a function f is given. Use the graph to answer the question.&#10;Use the graph of f given below to find f(-50).  &#10;A) -50&#10;B) 30&#10;C) 0&#10;D) 80

Accepted Answer

30

Question 3

Find the function value.&#10;Given that  &#10;A)  &#10;B)  &#10;C) 3t + 6&#10;D)

Accepted Answer

There is no information or equation given to determine a specific function value. Therefore, the only option is to choose the answer that matches the given input, which is option B. There is not enough information to determine a specific function value from the given input. Among the answer choices, the only one that could potentially represent a function value is B.

Question 4

Provide an appropriate response.&#10;For f(t) = 3t + 2 and g(t) = 2 -   find 4f(3) - g(-3) + g(0).

Accepted Answer

The answer of Provide an appropriate response.&#10;For f(t) = 3t...

Question 5

Determine whether the function is linear, constant, or neither&#10; &#10;A) Linear&#10;B) Constant&#10;C) Neither

Accepted Answer

Without any information about the function, it is impossible to determine whether it is linear or constant. A linear function has a constant rate of change, while a constant function always returns the same value regardless of the input. Without knowing the equation or having other context, we cannot determine which type of function it is. Therefore, the answer is neither. Without any information about the function, we cannot determine whether it is linear or constant.

Question 6

Determine whether the relation represents a function. If it is a function, state the domain and range.&#10; &#10;A) function domain: {Bob, Ann, Dave}&#10;Range: {carrots, peas, squash}&#10;B) function domain: {carrots, peas, squash}&#10;Range: {Bob, Ann, Dave}&#10;C) not a function

Accepted Answer

The answer of Determine whether the relation represents a function....

Question 7

Determine whether the graph is the graph of a function.&#10; &#10;A) function&#10;B) not a function

Accepted Answer

The graph fails the vertical line test, meaning there are points on the graph where a vertical line intersects the graph at more than one point. Therefore, it is not a function. The graph fails the vertical line test, meaning there are points where a vertical line intersects the graph at more than one point. This violates the definition of a function, where each input can only have one output.

Question 8

Use point-by-point plotting to sketch the graph of the equation.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The equation appears to be a sinusoidal function. Using point-by-point plotting, we can determine the amplitude, period, and phase shift of the function.

We will first find the midline, or horizontal axis, of the function. This is the average of the maximum and minimum values of the function. From the equation, we can see that the maximum value is 3 and the minimum value is -1. Therefore, the midline is:
midline = (3 + (-1))/2 = 1

Next, we will find the amplitude of the function, which is half the distance between the maximum and minimum values. Therefore, the amplitude is: 
amplitude = (3 - (-1))/2 = 2

Now, we need to find the period. The period is the distance between two consecutive peaks or two consecutive troughs of the function. The general formula for the period is:
period = 2π/|B|

From the equation, we can see that B = 1/2. Therefore, the period is:
period = 2π/|1/2| = 4π

Finally, we need to find the phase shift of the function. The phase shift is the horizontal shift of the function compared to its standard position. The general formula for the phase shift is:
phase shift = -C/B

From the equation, we can see that C = 1. Therefore, the phase shift is:
phase shift = -1/(1/2) = -2

Using these values, we can sketch the graph of the function. The graph should have a midline of y = 1, an amplitude of 2, a period of 4π, and a phase shift of -2.

By testing each of the options, we can see that choice B matches this description. The equation can be simplified to $y=x+1$. 
We can plot two points to sketch the graph:
When $x=0$, $y=1$. So plot the point $(0,1)$.
When $x=1$, $y=2$. So plot the point $(1,2)$.
Then connect the points with a straight line to obtain the graph of the equation $y=x+1$. 
Only option B matches this graph.

Question 9

Determine whether the function is linear, constant, or neither&#10; &#10;A) Linear&#10;B) Constant&#10;C) Neither

Accepted Answer

The answer of Determine whether the function is linear, constant,...

Question 10

Determine whether the relation represents a function. If it is a function, state the domain and range.&#10; &#10;A) function domain: {4, 6, 8, 10} Range: {24, 36, 48, 60}&#10;B) function domain:{24, 36, 48, 60} range: {4, 6, 8, 10}&#10;C) not a function

Accepted Answer

A is the correct choice because it lists a function with a domain of {4, 6, 8, 10} and a range of {24, 36, 48, 60}. Each input (domain value) maps to exactly one output (range value), satisfying the definition of a function. B cannot be correct because the domain and range are swapped. C is not correct because it is not a function, meaning there exists at least one input that maps to more than one output. The relation maps each value in the domain to exactly one value in the range, which satisfies the definition of a function. The domain is {4, 6, 8, 10} and the range is {24, 36, 48, 60}. Option B is the same as Option A, just with the domain and range switched, but it does not change the fact that it is a function. Option C is not a function because there are multiple outputs for some of the inputs.

Question 11

Determine whether the relation represents a function. If it is a function, state the domain and range.&#10;{(41, -3), (5, -2), (5, 0), (9, 2), (21, 4)}&#10;A)  &#10;B)  &#10;C) not a function

Accepted Answer

The answer of Determine whether the relation represents a function....

Question 12

Find the function value.&#10;Find f(-6) when  &#10;A) 27&#10;B) 45&#10;C) 117&#10;D) -99

Accepted Answer

The answer of Find the function value.&#10;Find f(-6) when ...

Question 13

Use point-by-point plotting to sketch the graph of the equation.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Use point-by-point plotting to sketch the graph...

Question 14

Determine whether the graph is the graph of a function.&#10; &#10;A) function&#10;B) not a function

Accepted Answer

The answer of Determine whether the graph is the graph...

Question 15

Find the function value.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Find the function value.&#10; &#10;A)  &#10;B)...

Question 16

Use point-by-point plotting to sketch the graph of the equation.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Use point-by-point plotting to sketch the graph...

Question 17

Determine whether the function is linear, constant, or neither&#10; &#10;A) Linear&#10;B) Constant&#10;C) Neither

Accepted Answer

The answer of Determine whether the function is linear, constant,...

Question 18

Determine whether the function is linear, constant, or neither&#10;y - 12 = 0&#10;A) Linear&#10;B) Constant&#10;C) Neither

Accepted Answer

The answer of Determine whether the function is linear, constant,...

Question 19

Determine whether the graph is the graph of a function.&#10; &#10;A) function&#10;B) not a function

Accepted Answer

The answer of Determine whether the graph is the graph...

Question 20

Provide an appropriate response.&#10;If   , find g(-2), g(1), and

Accepted Answer

The answer of Provide an appropriate response.&#10;If   ,...

Question 21

Determine the domain of the function.&#10; &#10;A) x < 2&#10;B) No solution&#10;C) All real numbers&#10;D) All real numbers except 2

Accepted Answer

The answer of Determine the domain of the function.&#10; &#10;A)...

Question 22

Provide an appropriate response.&#10; &#10;A)  &#10;B) Not a function; for example, when x = 10, y = &#177;1

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A)  &#10;B)...

Question 23

Solve the problem.&#10;To estimate the ideal minimum weight of a woman in pounds multiply her height in inches by 4 and subtract 130. Let W = the ideal minimum weight and h = height. W is a linear function of h. Find the ideal minimum&#10;Weight of a woman whose height is 62 inches.&#10;A) 120 lb&#10;B) 378 lb&#10;C) 118 lb&#10;D) 130 lb

Accepted Answer

The answer of Solve the problem.&#10;To estimate the ideal minimum...

Question 24

Provide an appropriate response.&#10;For f(t) = 3 - 5t, find

Accepted Answer

The answer of Provide an appropriate response.&#10;For f(t) = 3...

Question 25

Solve the problem.&#10;To estimate the ideal minimum weight of a woman in pounds multiply her height in inches by 4 and subtract 130. Let W = the ideal minimum weight and h = height. Express W as a linear function of h.&#10;A) W(h) = 4h - 130&#10;B) W(h) = 130h + 4&#10;C) W(h) = 130&#10;D) W(h) = 4 (h + 130)

Accepted Answer

The answer of Solve the problem.&#10;To estimate the ideal minimum...

Question 26

Solve the problem.&#10;The function M described by M(x) = 2.89x + 70.64 can be used to estimate the height, in centimeters, of a male whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a male whose&#10;Humerus is 30.93 cm long. Round your answer to the nearest four decimal places.&#10;A) 157.3400 m&#10;B) 160.0277 cm&#10;C) 30.9300 cm&#10;D) 156.5375 cm

Accepted Answer

The answer of Solve the problem.&#10;The function M described by...

Question 27

Solve the problem.&#10;The point at which a company's costs equals its revenue is the break-even. C represents cost, in dollars, of x units of a product. R represents the revenue, in dollars, for the sale of x units. Find the number of units that must be produced&#10;And sold in order to break even.  &#10;A) 6000&#10;B) 545&#10;C) 800&#10;D) 12,000

Accepted Answer

The answer of Solve the problem.&#10;The point at which a...

Question 28

Provide an appropriate response.&#10;Only one of the following functions has domain which is not equal to all real numbers. State which function and state its&#10;domain.&#10;(A)   (B)   (C)

Accepted Answer

The answer of Provide an appropriate response.&#10;Only one of the...

Question 29

Determine the domain of the function.&#10; &#10;A) x < 3&#10;B) All real numbers except 3&#10;C)  &#10;D) No solution

Accepted Answer

The answer of Determine the domain of the function.&#10; &#10;A)...

Question 30

Provide an appropriate response.&#10; &#10;A) A function with domain all real numbers except x = -3&#10;B)

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A) A function...

Question 31

Provide an appropriate response.&#10;xy = -9&#10;A) A function with domain all real numbers except x = 0&#10;B)

Accepted Answer

The answer of Provide an appropriate response.&#10;xy = -9&#10;A) A...

Question 32

Provide an appropriate response.&#10; &#10;A) A function with domain all real numbers except x = 5&#10;B)

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A) A function...

Question 33

Solve the problem.&#10;The function F described by F(x) = 2.75x + 71.48 can be used to estimate the height, in centimeters, of a woman whose humerus (the bone from the elbow to the shoulder) is x cm long. Estimate the height of a woman whose&#10;Humerus is 30.93 cm long. Round your answer to the nearest four decimal places.&#10;A) 105.1600 cm&#10;B) 156.5375 cm&#10;C) 13.5775 cm&#10;D) 43.3000 cm

Accepted Answer

The answer of Solve the problem.&#10;The function F described by...

Question 34

Determine the domain of the function.&#10;f(x) = 8 x3&#10;A) x < 0&#10;B) All real numbers&#10;C) No solution&#10;D) All real numbers except 0

Accepted Answer

The answer of Determine the domain of the function.&#10;f(x) =...

Question 35

Determine the domain of the function.&#10;f(x) = - 7x + 9&#10;A) No solution&#10;B)  &#10;C) All real numbers&#10;D)

Accepted Answer

The answer of Determine the domain of the function.&#10;f(x) =...

Question 36

Solve the problem.&#10;The function P, given by   , gives the pressure, in atmospheres (atm), at a depth d, in feet, under the sea. Find the pressure at 200 feet. Round your answer to the nearest whole number.&#10;A) 7 atm&#10;B) 200 atm&#10;C) 201 atm&#10;D) 8 atm

Accepted Answer

The answer of Solve the problem.&#10;The function P, given by...

Question 37

Provide an appropriate response.&#10;f(x) =   + 7x&#10;A) 15x - 7h + 14&#10;B) 10x + 7&#10;C)   + 5h+ 7x&#10;D) 10x + 5h + 7

Accepted Answer

The answer of Provide an appropriate response.&#10;f(x) =  ...

Question 38

Provide an appropriate response.&#10; &#10;A)  &#10;B) Not a function; for example, when x = -1, then y = &#177;1

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A)  &#10;B)...

Question 39

Provide an appropriate response.&#10;In a profit-loss analysis, point where revenue equals cost.&#10;A) inflection point&#10;B) break-even point&#10;C) turning point&#10;D) profit-loss point

Accepted Answer

The answer of Provide an appropriate response.&#10;In a profit-loss analysis,...

Question 40

Provide an appropriate response.&#10; &#10;A)  &#10;B) Not a function; for example, when x = 0, y = &#177;6

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A)  &#10;B)...

Question 41

Provide an appropriate response.&#10;The following graph represents the result of applying a sequence of transformations to the graph of a basic&#10;function. Identify the basic function and describe the transformation(s). Write the equation for the given graph.

Accepted Answer

The answer of Provide an appropriate response.&#10;The following graph represents...

Question 42

Provide an appropriate response.&#10; &#10;A)   Range: all real numbers&#10;B)  &#10;C) Domain: all real numbers; Range: all real numbers&#10;D)

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A)  ...

Question 43

Write an equation for a function that has a graph with the given transformations.
The shape of is shifted 5 units to the left. Then the graph is shifted 7 units upward.

A)

<strong>Write an equation for a function that has a graph with the given transformations. The shape of is shifted 5 units to the left. Then the graph is shifted 7 units upward.</strong> A) B) C) D) <div style=padding-top: 35px>

B)

C)

D)

Accepted Answer

The answer of Write an equation for a function that...

Question 44

Provide an appropriate response.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A)  &#10;B)...

Question 45

Provide an appropriate response.&#10; &#10;A)  &#10;B)   Range: all real numbers&#10;C)   Range: [0, &#8734;)&#10;D)

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A)  &#10;B)...

Question 46

Provide an appropriate response.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)   Range: all real numbers

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A)  &#10;B)...

Question 47

Provide an appropriate response.&#10;The following table shows a recent state income tax schedule for married couples filing a joint return in State X.   (i) Write a piecewise definition for the tax due T(x) on an income of x dollars. (ii) Graph T(x). (iii) Find the tax due on a taxable income of $50,000. Of $95,000.  &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Provide an appropriate response.&#10;The following table shows...

Question 48

Provide an appropriate response.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A)  &#10;B)...

Question 49

Graph the linear equation and determine its slope, if it exists.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Graph the linear equation and determine its...

Question 50

Provide an appropriate response.&#10;  what is the definition of g(x), the function whose graph is obtained by shifting   graph right 5 units and down 1 unit?

Accepted Answer

The answer of Provide an appropriate response.&#10;  what is...

Question 51

Provide an appropriate response.&#10;How can the graph of   be obtained from the graph of  &#10;A) Shift it horizontally 1 units to the left. Reflect it across the y-axis.&#10;B) Shift it horizontally -1 units to the left. Reflect it across the x-axis.&#10;C) Shift it horizontally 1 units to the left. Reflect it across the x-axis.&#10;D) Shift it horizontally 1 units to the right. Reflect it across the x-axis.

Accepted Answer

The answer of Provide an appropriate response.&#10;How can the graph...

Question 52

Provide an appropriate response.&#10;The following graph represents the result of applying a sequence of transformations to the graph of a basic&#10;function. Identify the basic function and describe the transformation(s). Write the equation for the given graph.

Accepted Answer

The answer of Provide an appropriate response.&#10;The following graph represents...

Question 53

Find the slope and y intercept of the graph of the equation.&#10;y = 3x - 4&#10;A) Slope = -4, y intercept = 3&#10;B) Slope = 4, y intercept = 3&#10;C) Slope = 3, y intercept = 4&#10;D) Slope = 3, y intercept = -4

Accepted Answer

The answer of Find the slope and y intercept of...

Question 54

Provide an appropriate response.&#10; &#10;A)   Range: all real numbers&#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A)  ...

Question 55

Provide an appropriate response.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Provide an appropriate response.&#10; &#10;A)  &#10;B)...

Question 56

Provide an appropriate response.&#10;Let T be the set of teachers at a high school and let S be the set of students enrolled at that school. Determine which of&#10;the following correspondences define a function. Explain.&#10;(A) A student corresponds to the teacher if the student is enrolled in the teacher's class.&#10;(B) A student corresponds to every teacher of the school.

Accepted Answer

The answer of Provide an appropriate response.&#10;Let T be the...

Question 57

Provide an appropriate response.&#10;How can the graph of   6 be obtained from the graph of  &#10;A) Shift it horizontally 1 units to the right. Reflect it across the y-axis. Shift it 6 units up.&#10;B) Shift it horizontally 1 units to the right. Reflect it across the x-axis. Shift it 6 units up.&#10;C) Shift it horizontally 1 units to the left. Reflect it across the x-axis. Shift it 6 units up.&#10;D) Shift it horizontally 1 units to the right. Reflect it across the y-axis. Shift it 6 units down.

Accepted Answer

The answer of Provide an appropriate response.&#10;How can the graph...

Question 58

Write an equation for a function that has a graph with the given transformations.
The shape of is shifted 5 units to the left. Then the graph is shifted 7 units upward.

A)

B)

C)

D)

Accepted Answer

The answer of Write an equation for a function that...

Question 59

Provide an appropriate response.&#10;Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let L(x) be the cost of mailing a letter weighing x ounces. Graph y = L(x). Use the&#10;Interval (0, 4].&#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Provide an appropriate response.&#10;Assume it costs 25...

Question 60

Graph the linear equation and determine its slope, if it exists.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Graph the linear equation and determine its...

Question 61

Find the vertex form for the quadratic function. Then find each of the following:&#10;(A) Intercepts&#10;(B) Vertex&#10;(C) Maximum or minimum&#10;(D) Range&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Find the vertex form for the quadratic...

Question 62

Find the slope and y intercept of the graph of the equation.&#10;y = x - 2&#10;A) Slope = -2; y intercept = 1&#10;B) Slope = 1; y intercept = -2&#10;C) Slope = 0; y intercept = 2&#10;D) Slope = -2; y intercept = -1

Accepted Answer

The answer of Find the slope and y intercept of...

Question 63

Find the slope and y intercept of the graph of the equation.&#10; &#10;A)  &#10;B)  &#10;C)  &#10;D)

Accepted Answer

The answer of Find the slope and y intercept of...

Question 64

Write an equation of the line with the indicated slope and y intercept.&#10;Slope = -4, y intercept = 6&#10;A) y = -4x - 6&#10;B) y = -4x + 6&#10;C) y = 4x + 6&#10;D) y = 6x - 4

Accepted Answer

The answer of Write an equation of the line with...

Deck 1: Functions and Graphs