Deck 1: Functions and Graphs

Question 1

Let A represent the amount of money Paul has in his
pocket. Paul and his girl friend go out to dinner. They
spend x dollars on food, pay 8% tax on the dinner
check, and leave a 15% tip (not including the tax).
(a) Write a function relating the amount of money in
Paul's pocket to the amount they spend on food for
dinner.
(b) If Paul has $46 in his pocket, what is the maximum
amount they could spend on food for dinner?
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FORM A DATE
1 Chapter Test NAMES
Directions: Show all work where appropriate. A graphing calculator may be necessary to answer
some questions.

Answer 1

Question 2

Find the inverse relation of

Answer 2

Question 3

The graph of which of the following functions is bounded above by x=2?

A)
B)
C)
D)
E)

Answer 3

Question 4

Solve algebraically and support graphically. Identify all extraneous solutions.

Question 5

Write the equation whose graph can be obtained from the graph of by a vertical stretching of factor 4 , a reflection through the x -axis, and a vertical shift 5 units up.

Question 6

Solve
by using the quadratic formula. Give your answer to one decimal place.

Question 7

A rectangular field is to be enclosed by a fence. An
existing fence will form one side of the enclosure. The
amount of new fence bought for the other three sides is
1200 feet. What is the maximum area of the enclosed
field?
formula. Give your answer to one decimal place.

Question 8

Alfred receives a salary of $2500 per month, and he
pays $550 per month in rent. What percentage of his
salary is spent on rent?

Question 9

Let
Find an equation for g , the reflection of f across the y -axis.

Question 10

Find the range of the function Give your answer in interval notation.

Question 11

Which of these functions is one-to-one?

A)
B) f(x)=6x +14
C)
D)
E)

Question 12

Give an example of a discontinuous function and state
why it is discontinuous.

Question 13

The graph to the right is a slight variation of one of the ten basic functions. Which of the following equations best represents the graph?

A)
B)
C)
D)
E)

Question 14

Write an equation that models the following and solve.
How many gallons of vanilla ice cream with 12%
butterfat must be mixed with 20 gallons of chocolate ice
cream with 20% butterfat to make vanilla fudge ice
cream with 15% butterfat?

Question 15

Question 16

Suppose the point (3, -5) lies on a graph of an even
function. Determine a second point on the graph.

Question 17

Find the domain of the function Give your answer in interval notation.

Question 18

What two functions implicitly define the relation What is the domain?

Question 19

(a) Find all the zeroes for the function
(b) List the intervals where the function is increasing.

Question 20

Describe how the graph of can be transformed to the graph of

Question 21

Question 22

Question 23

Let
(a) Why does have an inverse that is a function?
(b) Find a rule for and state its domain.

Question 24

Describe how the graph of can be obtained from the graph of

Question 25

ch01_p7_12 3/31/10 8:49 AM

Question 26

Question 27

Determine the domain of the real-valued function f(x)= ln (4-x) .

A)
B)
C)
D)
E)

Question 28

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FORM A
1 Chapter Test (continued) NAME

Question 29

Solve the equation Give exact answers.

Question 30

Determine the domain of the real-valued function f(x)=ln (x-4) .

A)
B)
C)
D)
E)

Question 31

Juan drives in city traffic for 2 hours. He travels 62 miles during that time. He averages 26 miles per hour less on this drive than he does on a country highway. What is his average speed on the country highway?

Question 32

Find all vertical and horizontal asymptotes of the graph of

Question 33

Find all vertical and horizontal asymptotes of the graph of

Question 34

Let and Find the function Give the domain of

Question 35

Three of the twelve basic functions are even functions. Which are they?

Question 36

Angela drives on a county highway for 2 hours. She travels 112 miles during this time. She averages 22 mph faster on this drive than she does in the city traffic. What is her average speed in the city?

Question 37

Use a graphing calculator to determine all local maxima and/or minima for the function Give the values where the extremum occur to two decimal places.

Question 38

A ball is hit straight up from a height of 3 ft with an initial velocity of 60 ft/sec . Write a set of parametric equations that you would use to graph height against time. Then find the maximum height of the ball and the number of seconds to reach that height.

Question 39

(a) Graph the piecewise function

(b) Is the function continuous? Why or why not?

Question 40

Solve the equation Give exact solutions.

Question 41

What are the upper and lower bounds for the function f(x)=cos x-1 ?

Question 42

A cylindrical tank with diameter 25 meters is filled with gasoline to a depth of 40 meters. The gasoline begins draining at a constant rate of 4 cubic meters per second. Write the volume of gasoline remaining in the tank t seconds after the tank begins draining as a function of t .

Question 43

Use a graphing calculator to determine all local maxima and/or minima for the function Give the values where the extremum occur to two decimal places.

Question 44

Let
(a) Why does have an inverse that is a function?
(b) Find a rule for

Question 45

Question 46

Five of the twelve basic functions are odd functions. Which are they?

Question 47

Let and
Find the function Give the domain of

Question 48

Describe how the graph of can be obtained from the graph of

Question 49

Question 50

A ball is hit straight up from a height of 4 ft with an initial velocity of 65 ft/sec. Write a set of parametric equations that you would use to graph height against time. Then find the maximum height of the ball and the number of seconds to reach that height.