Deck 7: Prerequisites

Question 1

​Find . ​ ​
​

A)
B)
C)
D)
E)

Answer 1

Question 2

Evaluate the indicated function for and . ​ ​
​

A)
B)
C)
D)
E)

Answer 2

Question 3

Find (f - g)(x). ​ ​

A)
B)
C)
D)
E)

Answer 3

Question 4

Find . ​ ​

A)
B)
C)
D)
E)

Question 5

Evaluate the indicated function for and . ​ ​
​

A)48
B)39
C)9
D)0
E)-39

Question 6

​Find . ​ ​

A)
B)
C)
D)
E)

Question 7

Evaluate the indicated function for and . ​ ​

A)12
B)-10
C)7
D)14
E)10

Question 8

​​​Evaluate the indicated function for and . ​ ​
​

A)
B)
C)
D)
E)

Question 9

Find (f + g)(x). ​ ​

A)
B)
C)
D)
E)

Question 10

Find (f + g)(x). ​ ​

A)
B)
C)
D)
E)

Question 11

Find (f + g)(x). ​ ​

A)2x
B)4x
C)-4x
D)-2x
E)2x + 8

Question 12

​Evaluate the indicated function for and . ​ ​
​

A)92
B)90
C)-86
D)89
E)91

Question 13

​​Evaluate the indicated function for and . ​ ​
​

A)30
B)
C)
D)
E)

Question 14

Find . ​ ​

A)
B)
C)
D)
E)

Question 15

Find . ​ ​

A)
B)
C)
D)
E)

Question 16

Find (f / g)(x).What is the domain of f / g? ​ ​

A) ; all real numbers x.
B) ; all real numbers x except x = 0
C) ; all real numbers x except x =
D) ; all real numbers x except x = 0
E) ; all real numbers x except x =

Question 17

Find (fg)(x). ​ ​

A)
B)
C)
D)
E)

Question 18

Find . ​ ​

A)
B)
C) ​
D)
E)

Question 19

Evaluate the indicated function for and . ​ ​
​

A)28
B)38
C)-38
D)125
E)17

Question 20

Find (f - g)(x). ​ ​

A)2x - 6
B)6
C)2x - 3
D)2x + 6
E)2x

Question 21

The research and development department of an automobile manufacturer has determined that when a driver is required to stop quickly to avoid an accident, the distance (in feet) the car travels during the driver's reaction time is given by , where x is the speed of the car in miles per hour.The distance (in feet) traveled while the driver is braking is given by .Find the function that represents the total stopping distance T. ​

A)
B)
C)
D)
E)

Question 22

​Find and the domain of the composite function. ​ ​

A) Domain of : all real numbers x except
B) Domain of : all real numbers x except
C) Domain of : all real numbers x except
D) Domain of : all real numbers x except
E) Domain of : all real numbers x except

Question 23

Find and the domain of the composite function. ​ ​

A) Domain of : all real numbers x
B) Domain of : all real numbers x
C) Domain of : all real numbers x
D) Domain of : all real numbers x
E) Domain of : all real numbers x

Question 24

From 2003 through 2008, the sales (in thousands of dollars) for one of two restaurants owned by the same parent company can be modeled by ​ ​
Where t = 3 represents 2003.During the same six-year period, the sales (in thousands of dollars) for the second restaurant can be modeled by
​ ​
Write a function that represents the total sales of the two restaurants owned by the same parent company.
​

A)​
B)​
C)​
D)​
E)​

Question 25

Find and the domain of the composite function. ​ ​

A) Domain of : all real numbers x
B) Domain of : all real numbers x
C) Domain of : all real numbers x
D) Domain of : all real numbers x
E) Domain of : all real numbers x

Question 26

Find and the domain of the composite function. ​ ​

A) Domain of : all real numbers x
B) Domain of : all real numbers x
C) Domain of : all real numbers x
D) Domain of : all real numbers x
E) Domain of : all real numbers x

Question 27

The weekly cost C of producing units x in a manufacturing process is given by .The number of units x produced in t hours is given by . ​
Find the cost of the units produced in 6 hours.
​

A)11,855
B)11,850
C)11,846
D)13,350
E)11,854

Question 28

The number of people playing tennis T (in millions) in the United States from 2000 through 2007 can be approximated by the function ​ ​
And the U.S.population P (in millions) from 2000 through 2007 can be approximated by the function , where t represents the year, with t = 0 corresponding to 2000.
Evaluate the function for t = 0 and 3.

A)h(0) = 0.1060, h(3) = 0.0783
B)h(0) = 0.3060, h(3) = 0.2783
C)h(0) = -0.2060, h(3) = -0.1783
D)h(0) = 0.1783, h(3) = 0.2060
E)h(0) = -0.1060, h(3) = -0.0783

Question 29

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles.The radius (in feet) of the outer ripple is , where t is the time in seconds after the pebble strikes the water.The area of the circle is given by the function .Find and interpret . ​

A) ; represents the area of the circle at time t.
B) ; represents the area of the circle at time t.
C) ; represents the area of the circle at time t.
D) ; represents the area of the circle at time t.
E) ; represents the area of the circle at time t.

Question 30

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models ​ and ​
Where t represents the year, with t = 0 corresponding to 2000.
​
Find and interpret .
​

A) , which represents the total number of Navy and Marines personnel combined.
B) , which represents the total number of Navy and Marines personnel combined.
C) , which represents the total number of Navy and Marines personnel combined.
D) , which represents the total number of Navy and Marines personnel combined.
E) , which represents the total number of Navy and Marines personnel combined.

Question 31

Find and the domain of the composite function. ​ ​

A) Domain of : all real numbers x except
B) Domain of : all real numbers x except
C) Domain of : all real numbers x except
D) Domain of : all real numbers x except
E) Domain of : all real numbers x except

Question 32

Find (f + g)(x).​ ​ ​
​

A)​
B)​
C)​
D)​
E)​

Question 33

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models ​ and ​
Where t represents the year, with t = 0 corresponding to 2000.
Find and interpret .
​

A) , which represents the difference between the number of Navy personnel and the number of Marines personnel.
B) , which represents the difference between the number of Navy personnel and the number of Marines personnel.
C) , which represents the difference between the number of Navy personnel and the number of Marines personnel.
D) , which represents the difference between the number of Navy personnel and the number of Marines personnel.
E) , which represents the difference between the number of Navy personnel and the number of Marines personnel.

Question 34

Find and the domain of the composite function. ​ ​
​

A) Domain of : all real numbers x
B) Domain of : all real numbers x
C) Domain of : all real numbers x
D) Domain of : all real numbers x
E) Domain of : all real numbers x

Question 35

Consider the functions and . ​
Find .
​

A)
B)
C)
D)
E)

Question 36

The spread of a contaminant is increasing in a circular pattern on the surface of a lake.The radius of the contaminant can be modeled by , where r is the radius in meters and t is the time in hours since contamination. ​
Find a function that gives the area A of the circular lake in terms of the time since the spread began.
​

A)
B)
C)
D)
E)

Question 37

The suggested retail price of a new hybrid car is p dollars.The dealership advertises a factory rebate of $2000 .
​
Select a function R in terms of p giving the cost of the hybrid car after receiving the rebate from the factory.
​

A)
B)
C)
D)
E)

Question 38

The number N of bacteria in a refrigerated food is given by where T is the temperature of the food in degrees Celsius.When the food is removed from refrigeration, the temperature of the food is given by where t is the time in hours. Find the bacteria count after 0.5 hour.
​

A)About 565 bacteria
B)About 793 bacteria
C)About 653 bacteria
D)About 390 bacteria
E)About 705 bacteria

Question 39

Find ( f / g )(x). ​

A)
B)
C)
D) ​
E)

Question 40

The number of people playing tennis T (in millions) in the United States from 2000 through 2007 can be approximated by the function ​ ​
And the U.S.population P (in millions) from 2000 through 2007 can be approximated by the function , where t represents the year, with t = 0 corresponding to 2000.
Find .
​

A) ​
B) ​
C)
D) ​
E)

Question 41

Let f (x) = 2x + 1, g(x) = 3x - 2.Find the function. ​ ​

A)
B)
C)
D)
E)none of the above

Question 42

The monthly cost C of running the machinery in a factory for t hours is given by ​ The number of hours t needed to produce x products is given by .
Find the equation representing the cost C of manufacturing x products.

A)
B)
C)
D)
E) ​

Question 43

Evaluate the indicated function for and . ( fg )(1)

A)15
B)-35
C)-23
D)-25
E)-33

Question 44

Find ( fg )(x).

A)
B)
C)
D)
E)

Question 45

Find ( f − g )(x). ​

A)
B)
C)
D)
E)

Question 46

Evaluate the indicated function for and . ​

A)​
B)​
C)​
D)​
E)​

Question 47

Find . ​ ​

A)
B)
C)
D)
E)

Question 48

Use the graphs of f and g to evaluate the function.

A)1
B)-2
C)4
D)-1
E)2

Question 49

For following function, select (on the same set of coordinate axes) a graph for . ​ ​

A)​
B)​
C)​
D)​
E)​

Question 50

Let f (x) = 2x + 1, g (x) = 3x - 2.Find the function.
​ ​
Please give the answer as a simplified expression (not an equation).

Question 51

For following function, select (on the same set of coordinate axes) a graph for . ​ ​

A)​
B)​
C)​
D)​
E)​

Question 52

Let .Find the composite function which expresses the given correspondence correctly. ​ ​

A)
B)
C)
D)
E)none of the above

Question 53

For following function, select (on the same set of coordinate axes) a graph for . ​ ​

A)​
B)​
C)​
D)​
E)​

Question 54

Use the given graph of f to select the graph for the following function. ​ ​ ​

A)​
B)​
C)​
D)​ ​
E)​

Question 55

Find . ​ ​

A)
B)
C)
D)
E)

Question 56

Find .

A)
B)
C)
D)
E)

Question 57

For following function, select (on the same set of coordinate axes) a graph of function for . ​ ​

A)​
B)​
C)​
D)​
E)​

Question 58

Use the given graph of f to select the graph for the following function. ​
Y = f(2x)
​ ​

A)​
B)​
C)​
D)​
E)​

Question 59

Let f (x) = 2x - 1, g(x) = 3x - 2.Find the domain of the function. ​ ​

A)
B)
C)
D)
E)

Question 60

Find . ​ ​

A)
B)
C) ​
D)
E)

Question 61

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph. ​
​ ​

A)Vertical stretch of
B)Horizontal stretch of
C)Vertical stretch of
D)Vertical stretch of
E)Horizontal stretch of

Question 62

Use the graph of to write an equation for the function whose graph is shown. ​ ​

A)
B)
C)
D)
E)

Question 63

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph. ​ ​

A)Reflection in the x-axis of
B)Horizontal shift of x-axis of
C)Reflection in the y-axis of
D)Horizontal shift of x-axis of
E)Reflection in the y-axis of

Question 64

Use the graph of to write an equation for the function whose graph is shown. ​
​ ​

A)
B)
C)
D)
E)

Question 65

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph. ​ ​

A)Horizontal shift of
B)Vertical shift of
C)Vertical shift of
D)Horizontal shift of
E)Vertical shift of

Question 66

Use the graph of to write an equation for the function whose graph is shown. ​
​ ​

A)
B)
C)
D)
E)

Question 67

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph. ​ ​

A)Reflection in the x-axis and vertical shift of
B)Vertical shift of x-axis and vertical shift of
C)Reflection in the x-axis and vertical shift of
D)Horizontal shift of x-axis and vertical shift of
E)Horizontal shift of x-axis and vertical shift of

Question 68

Use the given graph of f to select the graph for following function. ​ ​
​ ​

A)​
B)​
C)​
D)​
E)​

Question 69

Use the graph of to write an equation for the function whose graph is shown. ​
​ ​

A)
B)
C)
D)
E)

Question 70

Write an equation for the function that is described by the given characteristic. ​
The shape of , but shifted 17 units to the right.
​

A)
B)
C)
D)
E)

Question 71

Use the graph of to write an equation for the function whose graph is shown. ​
​ ​

A)
B)
C)
D)
E)

Question 72

Use the graph of to write an equation for the function whose graph is shown. ​ ​

A)
B)
C)
D)
E)

Question 73

Use the graph of to write an equation for the function whose graph is shown. ​ ​

A)​
B)
C)
D)
E)None of the above

Question 74

Write an equation for the function that is described by the given characteristic. ​
The shape of , but shifted three units to the left and reflected in both the x-axis and the y-axis.
​

A)
B)
C)
D)
E)

Question 75

Use the graph of to write an equation for the function whose graph is shown. ​
​ ​

A)
B)
C)
D)
E)

Question 76

Identify the parent function and the transformation shown in the graph.Write an equation for the function shown in the graph. ​ ​

A)Horizontal shift of the x-axis of
B)Vertical shift of the y-axis of
C)Reflection in the x-axis of
D)Horizontal shift of the y-axis of
E)Vertical shift of the x-axis of

Question 77

Use the given graph of f to select the graph for following function. ​ ​

A)​
B)​
C)​
D)​
E)​

Question 78

Use the graph of to write an equation for the function whose graph is shown. ​
​ ​

A)
B)
C)
D)
E)

Question 79

Use the graph of to write an equation for the function whose graph is shown. ​ ​

A)
B)
C)
D)
E)

Question 80

Write an equation for the function that is described by the given characteristic. ​
The shape of , but shifted three units to the right and five units downward.
​

A)
B)
C)
D)
E)