Deck 2: Functions

Question 1

A model rocket is launched from the roof of a building. For height h, in meters, and time t, in seconds, after the rocket is launched, the height of the rocket above the ground is given by . Is the graph of concave up or concave down?

Answer 1

concave down

Question 2

The number of cancer cells in a patient grows slowly at first, but then grows with increasing rapidity. Does the following figure accurately represent the number of cancer cells in a patient graphed against time?

Answer 2

True

Question 3

Which scenario below best matches the following graph?

A) The price of memory chips isn't decreasing as quickly as it used to be.
B) The cost of a new car is increasing at an ever increasing rate.
C) The annual profits made by Upper Midwest Industries are decreasing at a higher rate each year.
D) The medication is slowing the rise of a child's temperature.

Answer 3

The price of memory chips isn't decreasing as quickly as it used to be.

Question 4

Calculate successive rates of change for the function Shown in the following table to determine if the graph is more likely concave up or concave down for

A) concave up
B) concave down
C) neither

Question 5

Calculate successive rates of change for the function Shown in the following table to determine if the graph is more likely concave up or concave down for

A) concave up
B) concave down
C) neither

Question 6

Does the following figure appear to be concave up, concave down, or neither?

Question 7

Does the graph of appear to be concave up, concave down, or neither?

Question 8

The quantity of the drug in a patient's bloodstream increased at a decreasing rate until it reached saturation. Which of the following graphs shows the quantity of drug in the blood graphed against time?

A)

B)

C)

D)

E)

F)

Question 9

The rumor spread slowly--then faster--then slowly again. Which of the following statements describes the graph of number of people who have heard the rumor against time?

A)Increasing and concave up
B)Decreasing and concave up
C)Increasing and concave down
D)Decreasing and concave down
E)None of the above

Question 10

Determine the concavity of the graph of between x = 0 and x = 3 by calculating average rates of change over intervals of length 1. Is the graph concave up or concave down?

Question 11

The car slowed down steadily. Which of the following tables of values could represent

A)
B)
C)
D)
E)

Question 12

Sketch a graph of so that will have all of the following properties:

Question 13

Graph and use the graph to give an estimate of the largest interval on which the function is concave up.

Question 14

The graph of Is concave down for . Which of the following is the largest?

A)
B)

Question 15

Question 16

If is decreasing and concave up on , then
.

Question 17

If Is decreasing and concave down on , which of the following must be true.

A)

B)

C)

D)

Question 18

Use the following chart containing values of to determine whether the function appears to be:
a) increasing or decreasing
b) concave up or concave down

Question 19

Use the following chart containing values of to determine whether the function appears to be:
a) increasing or decreasing
b) concave up or concave down

Question 20

It is possible for the graph of a function to be decreasing and concave up on the interval and decreasing and concave down on the interval

.

Question 21

The probability of being in an accident increases as a driver's blood-alcohol content (BAC) rises. It has been observed that the probability rises faster and faster as the BAC increases. Let ^P(x) be the probability that a driver will be involved in an accident as a function of x, the driver's BAC. Let L be the BAC at or above which it is illegal to drive. Let ^{b = P(0)} What is the meaning of
P^-1(6b) ?

A) The probability of an accident for someone who has had 6 drinks.
B) 6 times the probability of an accident for someone who hasn't been drinking.
C) The BAC at which the probability of an accident is 6 times that of a person who hasn't been drinking.
D) The BAC at which the probability of an accident is 6 times that of a person whose BAC is at the legal level.

Question 22

The function Gives the weekly demand for DVD rentals at Joe's Videolog when Joe charges $p to rent a DVD. What does
mean in practical terms?

A) The number of rentals demanded if Joe charges $70 per rental.
B) The rental fee Joe must charge to get a weekly demand of 70 rentals.
C) The profit Joe makes if he charges $70 per rental.
D) The rental fee Joe must charge to get a profit of $70.

Question 23

What are the units of ( W ) if W
is the average weight, in pounds, of a baby t months old?

Question 24

Use the graph of Given below to estimate (Mark all correct answers)

A) 3.5
B) -3.5
C) 6.5
D) -6.5
E) -1.5
F)1 .5

Question 25

Use the following figure to evaluate f ^-1(-3).

Question 26

Use the following table to evaluate f ^-1(0).

Question 27

Let Be a composite function, where Is the volume of oil, in cubic meters, that has leaked from a broken pipeline after t days, and
Is the cost, in dollars, of V cubic meters of oil. What are the units of ?

A) cubic meters
B) days
C) dollars

Question 28

If , what is the inverse function ?

A)
B)
C)
D)

Question 29

The circumference, in cm, of a circle whose radius is r cm is given C =2πr if V = f(r) evaluate and interpret f ^-1 (16 π )

A) 12π² ,the circumference of a circle with radius 6π
B) 12π² , the radius of a circle with circumference 6π
C) 4, the circumference of a circle with radius 6π .
D) 4, the radius of a circle with circumference 6π .

Question 30

Question 31

Suppose and are invertible functions such that , , , , ,and . Find
.

Question 32

Suppose and suppose that is an invertible function such that https://d2lvgg3v3hfg70.cloudfront.net/TB10073/. Find andwrite it in the form
.

Question 33

Suppose and suppose that is an invertible function such that . Find andwrite it in the form
.

Question 34

Let and be two invertible functions such that and . Find . Round your answer to two decimal places, if necessary.

Question 35

Let and be two invertible functions such that and . Find . Round your answer to two decimal places, if necessary.

Question 36

Let and be two invertible functions such that and . Find . Round your answer to two decimal places, if necessary.

Question 37

Let and be two invertible functions such that and . Find . Round your answer to two decimal places, if necessary.

Question 38

Let and . Find the domain of .

Question 39

Let and . Is in the domain of ?

Question 40

Let with the domain . Find the domain of

Question 41

Which of the following is the range of the function
?

A)
B)
C)
D) all real numbers

Question 42

Evaluate if

Question 43

Does the following figure show an accurate graph of ?

Question 44

ComGas, the Cambridge power company, charges its customers $7.77 a month, plus an additional $0.99 per therm up to 37 therms and $0.69 per therm above 37 therms. (A therm is a unit of gas supplied.) Let
Be the monthly cost in dollars for using x therms. Which of the following is the formula for C?

A)

B)

C)

D)

Question 45

A T-shirt printing company charges a set-up fee of $10 for each order, plus the cost per shirt shown in the table. Let C be the total cost in dollars for printing n shirts. Which of the following is the formula for C?

A)

B)

C)

D)

Question 46

Graph the function:

Question 47

Write a formula for the following function:

Question 48

Use the definition of absolute value to write a piecewise formula for
.

Question 49

Let . Evaluate:

Question 50

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $1.40. Let be the total cost if you need x cans of soda. What is ?

Question 51

In the following graph, is m a function of n?

Question 52

Fred's cell phone company charges $50 per month and $0.35 for each minute (or part of a minute) over 120 minutes.
a) Write a formula for the company's policy.
b) How much is Fred's cell phone bill for the month if he talks for 158 minutes.

Question 53

Fred's cell phone company charges $55 per month and $0.45 for each minute (or part of a minute) over 115 minutes. Which of the following is the domain of the function?

A)
B)
C)
D)

Question 54

Which of the following is a piecewise formula for the function

A)
B)
C)
D)

Question 55

Let
.
a) What is the domain of ?
b) What is the range of ?

Question 56

Let .


.

Question 57

For , what is ?

A)
B)
C)
D)

Question 58

Assume that height is a function of age and that Is the average height (in inches) for females in the US at age a years. What is the practical interpretation of ?

A) z plus the number of US females who are 20 inches tall.
B) 20 plus the number of US females who are z inches tall.
C) 20 years older than the average US female who is z inches tall.
D) 20 inches taller than the average height of a z year old US female.

Question 59

Which of the following is a piecewise defined function for ?

A)

B)

C)

D)

Question 60

Find a formula for the following graph:

Question 61

Let
a) Find the domain of

b) Find the range of

Question 62

Let

Graph the function.

Question 63

Let

a) Find the domain of
b) Find the range of

Question 64

Let

Question 65

Assume that height is a function of age and that Is the average height (in inches) for females in the US at age a years. What is the practical interpretation of
?

A) The number of US females who are 25 years old.
B) The number of US females who are 25 inches tall.
C) The average height of a US female who is 25 years old.
D) The average age of a US female who is 25 inches tall.

Question 66

Let Be the federal income tax paid based on a total taxable income of x dollars. The value ofIs approximated by the graph in the following figure. In this context, which of the following is greater?

A)
B)

Question 67

Let Be the federal income tax paid based on a total taxable income of x dollars. The value ofIs approximated by the graph in the following figure. Which of the following would represent an increase in your income tax if your income was w dollars?

A)
B)
C)
D)

Question 68

What is the range of
, where a is a constant?

A) x > -a
B) y > 0
C) y > 5
D) x > a

Question 69

Let https://d2lvgg3v3hfg70.cloudfront.net/TB10073/. What is the domain of
?

A)
B)
C) x < 0
D) x > 0

Question 70

Assume that height is a function of age and that Is the average height (in inches) for females in the US at age a years. What is a reasonable domain for
?

A)
B)
C)
D)

Question 71

Which of the following are not in the domain of ?

A) x = 7
B) x = -7
C) x = 6
D)
E)

Question 72

Which of the following are not in the range of
?

A) y = 4
B) y = -6
C) y = -2
D)
E)

Question 73

What is the domain of the function ?

A)
B)
C)
D)

Question 74

What is the range of the function ?

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

Question 75

The graph of Is shown below. What is the range of ?

A)
B)
C)
D)

Question 76

Assuming the entire graph of Is shown, what is the domain of ?

A)
B)
C)
D)

Question 77

Question 78

An organization has 200 raffle tickets to sell for $4 each. From the proceeds of the sale, they will award the winning ticket holder $50. The profit, P, that the organization receives is a function of the number, n, of tickets sold. Assuming they sell at least one ticket, the range of this function is

Question 79

A model rocket is launched from the roof of a building. For height h, in meters, and time t, in seconds, after the rocket is launched, the height of the rocket above the ground is given by

. The domain of this function is approximately Round to the nearest whole number.

Question 80

A model rocket is launched from the roof of a building. For height h, in meters, and time t, in seconds, after the rocket is launched, the height of the rocket above the ground is given by
Interpret the domain of the graph of ^{f (t)}

A) The time it takes for the rocket to hit the ground
B) The heights the rocket reaches
C) The rocket's initial height
D) The time the rocket is in the air
E) The maximum height obtained by the rocket.