Deck 10: Compositions, Inverses, and Combinations of Functions

Question 1

Let Be a linear function with a negative slope and Be a different linear function with a positive slope. Describe the graph of
.

A) A pair of curves that approach both a horizontal and a vertical asymptote.
B) A parabola that opens downward.
C) A parabola that opens upward.
D) Another linear function.

Answer 1

Another linear function.

Question 2

Let and for positive constants a and b. Let . If and , what is ?

Answer 2

50

Question 3

Is the quotient of two even functions odd, even, or neither?

Answer 3

even

Question 4

For , does ?

Question 5

The following table gives 3 functions, f, g, and h. Which of the following statements is true?

A)
B)
C)
D)
E)

Question 6

The following table gives 3 functions, f, g, and h.
Given that f is linear, use the relationships between f, g, and h to find aformula for h:

Question 7

The function Is shown in the first figure. Which transformation of is shown in the second figure?

A)
B)
C)
D)

Question 8

The following table gives values for the functions f, g, and h, three functions defined only for the values x = 0, 1, . . . , 5. Based on the table, what is ?

Question 9

Let and . What is ?

Question 10

The functions and are defined by the graph below. The dashed graph is and the solid graph is .
Evaluate .

Question 11

Let And What is ?

A)
B)
C)
D)

Question 12

Let And What is ?

A)
B)
C)
D)

Question 13

A)
B)
C)
D)

Question 14

Find if and .

Question 15

Let and Find a simplified formula for .

Question 16

Let and . Find a simplified formula for the function

Question 17

Let be the number of men and be the number of women residing in a certain town in year t. Let be the average income, in dollars, of residents of that town in year t. If and , find a simplified formula for the total amount of money earned by all adult residents of the town in year t.

Question 18

Let be the number of men and let be the number of women residing in a certain town in year t. Let be the average income, in dollars, of residents of that town in year t. If and , find a simplified formula for the total amount of money earned by all adult residents of the town in year 3.

Question 19

Find a simplified formula for h given

Question 20

Let Find and simplify

Question 21

Let . Does ?

Question 22

LetAnd let What is ?

A)
B)
C)
D)

Question 23

Given , what is ?

A)
B)
C)
D)

Question 24

Let and . Evaluate g .

Question 25

Let and . Evaluate g to 2 decimal places.

Question 26

Given the graph of g below, which of the following is a solution to the equation ?

A) 0
B) 2
C) 3
D) 1
E) -3

Question 27

Given the graph of f below, solve . If there is more than one answer, enter them from least to greatest, separated by semicolons. If there are no solutions, enter "none".

Question 28

Based on the following table, could the function be invertible?

Question 29

Is the function invertible if the domain of f is all negative real numbers?

Question 30

Is the function the inverse of the function ?

Question 31

For positive numbers x, what is the inverse of ?

A)
B)
C)
D)

Question 32

What is the inverse of ?

A)
B)
C)
D)

Question 33

Given , solve . Round to 3 decimal places.

Question 34

Given , solve .

Question 35

Given , does ?

Question 36

Let . Does ?

Question 37

Is the function graphed below invertible?

Question 38

Use a graph to determine whether or not is invertible.

A) It is not invertible
B) It is invertible

Question 39

Let give the annual profit of a company (in thousands of dollars) t years after its formation. What is ? Round to the nearest whole number and include units.

Question 40

The following figure defines a function f. Which of the following quantities is greater?

A)
B)

Question 41

Suppose What is the range of ?

A) All real numbers less than or equal to 0.
B) All real numbers greater than or equal to 0.
C) All real numbers less than or equal to 7.
D) All real numbers greater than or equal to 7.

Question 42

If , what is the value of C in the following tables?

Question 43

Let and . Evaluate
.

Question 44

The functions and are defined by the graph below. The dashed graph is and the solid graph is Evaluate
.

Question 45

If , which of the following could be true? Mark all that apply.

A)
B)
C)
D)
E)
F)

Question 46

The functions and are defined by the graph below. The dashed graph is and the solid graph is . If , what is ?

Question 47

Given the graphs of f and g below, evaluate f(g(3)).

Question 48

Let and . Using the table below gives and .

Question 49

Given And , what is g(f(x)?

A)
B)
C)
D)

Question 50

Let and . Does m(n(x)) = ?

Question 51

If , which of the following could be true? Mark all that apply.

A)
B)
C)
D)

Question 52

If and , does ?

Question 53

If And , what is ?

A)
B)
C)
D)

Question 54

Let And What is ?

A)
B)
C)
D)

Question 55

Let And What is ?

A)
B)
C)
D)

Question 56

Let f be defined by the following graph. Describe the graph of

A) A version of the graph of f reflected across the x-axis, compressed by a factor of 1/3.
B) A version of the graph of f reflected across the x-axis, stretched vertically by a factor of 3.
C) A version of the graph of f reflected across the y-axis, compressed by a factor of 1/3.
D) A version of the graph of f reflected across the y-axis, stretched vertically by a factor of 1/3..

Question 57

Let f be defined by the following graph. Describe the graph of
.

A) A version of the graph of f flipped about the y-axis and shifted up by 2 units.
B) A version of the graph of f flipped about the y-axis and shifted down by 2 units.
C) A version of the graph of f flipped about the x-axis and shifted down by 2 units.
D) A version of the graph of f flipped about the x-axis and shifted up by 2 units.

Question 58

Let . Does ?

Question 59

Let , and . Does ?

Question 60

Let and . Does ?

Question 61

Let and . Does ?

Question 62

Find for

Question 63

If , which of the following could be true? Mark all that apply.

A)
B)
C)
D)
E)

Question 64

A child building a tower with blocks places 20 blocks in the first row, 19 blocks in the second row, 18 blocks in the third row, and so forth. How many blocks are in the 11^th row?