Deck 4: Exponential and Logarithmic Functions

Question 1

Given the function f : = {(1, 2), (2, 3), (3, 4)} write the set of ordered pairs representing

Answer 1

{(2, 1), (3, 2), (4, 3)}

Question 2

Use the definition of a one-to-one function to determine if the function is one-to-one.

A) No
B) Yes

Answer 2

A

Question 3

A function defined by ) (is/is not) a one-to-one function if no horizontal line intersects the
graph of f in more than one point.

Answer 3

is

Question 4

The notation is often used to represent the inverse of a function f and not the reciprocal of
f.

Question 5

Determine if the relation defines y as a one-to-one function of x.

A) Yes
B) No

Question 6

Determine if the relation defines y as a one-to-one function of x.

A) Yes
B) No

Question 7

If no horizontal line intersects the graph of a function f in more than one point then f is a
- - function.

Question 8

Given a one-to-one function defined by

Question 9

Determine if the relation defines y as a one-to-one function of x.

A) Yes
B) No

Question 10

The function defined by is/is not) a one-to-one function, whereas 0 (is/is not) a one-to-one function.

Question 11

Determine if the relation defines y as a one-to-one function of x.

A) Yes
B) No

Question 12

Choose the one alternative that best completes the statement or answers the question.
A relation in x and y is given. Determine if the relation defines y as a one-to-one function of x.

A) Yes
B) No

Question 13

A function f is a - - function if for a and b in the domain of f, if

Question 14

Determine if the relation defines y as a one-to-one function of x.

A) Yes
B) No

Question 15

Choose the one alternative that best completes the statement or answers the question.
A relation in x and y is given. Determine if the relation defines y as a one-to-one function of x.

A) Yes
B) No

Question 16

Let f be a one-to-one function and let g be the inverse of f. Then and .

Question 17

The function

Question 18

The graph of a function and its inverse are symmetric with respect to the line ______.

Question 19

Choose the one alternative that best completes the statement or answers the question.
A relation in x and y is given. Determine if the relation defines y as a one-to-one function of x.

A) Yes
B) No

Question 20

If (a, b) is a point on the graph of a one-to-one function f, then the corresponding ordered pair
is a point on the graph of

Question 21

A one-to-one function is given. Write an expression for the inverse function.

Question 22

Solve the problem.

Question 23

Solve the problem.
There were 2,300 applicants for enrollment to the freshman class at a small college in the year 2010. The number of applicants has risen linearly by roughly 170 per year. The number of applications f
(x) is given by f (x) = 2,300 + 170x, where x is the number of years since 2010.
A) Determine if the function is the inverse of f.
B) Interpret the meaning of function g in the context of the problem.

A) a. Yes b. The value g(x) represents the number of years since the year 2010 based on the number of
Applicants to the freshman class, x.
B) a. No b. The value g(x) represents the number of applicants to the freshman class based on the number
Of years since 2010, x.
C) a. No b. The value g(x) represents the number of years since the year 2010 based on the number of
Applicants to the freshman class, x.
D) a. Yes b. The value g(x) represents the number of applicants to the freshman class based on the number
Of years since 2010, x.

Question 24

The graph of a function is given. Graph the inverse function.

Question 25

Given f (x), write an equation for ) and then graph f (x) and ) on the same coordinate system.

Question 26

A one-to-one function is given. Write an expression for the inverse function.

Question 27

Determine whether the two functions are inverses.

A) Yes
B) No

Question 28

A one-to-one function is given. Write an expression for the inverse function.

Question 29

Solve the problem.

Question 30

Use the definition of a one-to-one function to determine if the function is one-to-one.

A) No
B) Yes

Question 31

The graph of a function is given. Graph the inverse function.

Question 32

Find the inverse mentally.

Question 33

A one-to-one function is given. Write an expression for the inverse function.

Question 34

A one-to-one function is given. Write an expression for the inverse function.

Question 35

Determine whether the two functions are inverses.

A) No
B) Yes

Question 36

The graph of a function is given. Graph the inverse function.

Question 37

A one-to-one function is given. Write an expression for the inverse function.

Question 38

Solve the problem.

Question 39

Find the inverse mentally.

Question 40

Solve the problem.
The millage rate is the amount of property tax per $1000 of the taxable value of a home. For a certain county the millage rate is 29 mil. A city within the county also imposes a flat fee of $101 per
Home. x

Question 41

Choose the one alternative that best completes the statement or answers the question.
Evaluate the function at the given value of x. Round to 4 decimal places if necessary.

Question 42

Choose the one alternative that best completes the statement or answers the question.
Evaluate the function at the given value of x. Round to 4 decimal places if necessary.

Question 43

Choose the one alternative that best completes the statement or answers the question.
Evaluate the function at the given value of x. Round to 4 decimal places if necessary.

Question 44

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.

Question 45

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
All exponential functions pass through the point .

Question 46

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The graph of is (increasing/decreasing) over its domain.

Question 47

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The domain of an exponential function is .

Question 48

Graph the function and write the domain and range in interval notation.

Question 49

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The range of an exponential function is .

Question 50

Choose the one alternative that best completes the statement or answers the question.
Evaluate the function at the given value of x. Round to 4 decimal places if necessary.

Question 51

Solve the problem.

Question 52

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The horizontal asymptote of an exponential function is the line .

Question 53

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The graph of is (increasing/decreasing) over its domain.

Question 54

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.

Question 55

Choose the one alternative that best completes the statement or answers the question.
Evaluate the function at the given value of x. Round to 4 decimal places if necessary.

A) 6
B) 4.899
C) 5.4622
D) Undefined

Question 56

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The function is the exponential function base and is also called the
exponential function.

Question 57

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The formula gives the amount A in an account after t years at an interest rate r under the
assumption that interest is compounded .

Question 58

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.

Question 59

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
The function defined by (is/is not) an exponential function.

Question 60

Graph the function and write the domain and range in interval notation.

Question 61

Solve the problem.

Question 62

Graph the function and write the domain and range in interval notation.

Question 63

Solve the problem.

Question 64

Graph the function and write the domain and range in interval notation.

Question 65

Solve the problem.
The atmospheric pressure on an object decreases as altitude increases. If a is the height (in km) above sea level, then the pressure P(a) (in mmHg) is approximated by P(a) = 760e-0.13a. Determine
The atmospheric pressure at 7.176 km. Round to the nearest whole unit.

A) 4,789 mmHg
B) 261 mmHg
C) 299 mmHg
D) 379 mmHg

Question 66

Solve the problem.

Question 67

Use transformations of the graph to graph the function. Write the domain and range in interval
notation.

Question 68

Use transformations of the graph to graph the function. Write the domain and range in interval
notation.

Question 69

Solve the problem.

Question 70

Solve the problem.

Question 71

ng, in

Question 72

Evaluate the function at the given value of x. Round to 4 decimal places if necessary.

A) -5.4366
B) 6.5809
C) 0.6931
D) 0.1353

Question 73

ng, in

Question 74

Solve the problem.

Question 75

Solve the problem.
James wants to invest $8,000. He can invest the money at 7.2% simple interest for 30 yr or he can invest at 7% with interest compounded continuously for 30 yr. Which option results in more total
Interest?

A) 7% compounded continuously results in more total interest
B) 7.2% simple interest results in more total interest

Question 76

Solve the problem.
ation.

Question 77

Solve the problem.

Question 78

Use transformations of the graph to graph the function. Write the domain and range in interval
notation.

Question 79

Solve the problem.
Bethany needs to borrow $8,000. She can borrow money at 6.9% simple interest for 3 yr or she can borrow at 6.5% with interest compounded continuously for 3 yr. Which option results in less total
Interest?

A) 6.5% compounded continuously results in less total interest
B) 6.9% simple interest results in less total interest

Question 80

Solve the problem.