Test 1

Intro to Pre-Calculus and Applied Math Name: ___________________________

Relations and Functions

Multiple ChoiceIdentify the choice that best completes the statement or answers the question.

____ 1. Each point on this graph represents an animal. Which animal has the least mass?

AB

C D

E

F

G

Age (years)

Mas

s (k

g)

Ages and Masses of Animals

0 4 8 12 16 20

20

40

60

80

a. C b. A c. D d. E

____ 2. Joshua went on a bike ride. For part of the ride, Joshua stopped to play in a park with a friend. Which segment of the graph best describes this part of his bike ride?

Time (min)

Dis

tan

ce f

rom

ho

me

(km

)

Joshua's Bike Ride

O

A

B C

D

20 40 60 80 100 120

1

2

3

4

5

a. CD b. AB c. OA d. BC


____ 3. A person in a car drives away from a stop sign, cruises at a constant speed, and then slows down as she approaches another stop sign. Which graph best represents this situation?

a.

Time (min)

Sp

eed

(km

/h)

c.

Time (min)

Sp

eed

(km

/h)

b.

Time (min)

Sp

eed

(km

/h)

d.

Time (min)

Sp

eed

(km

/h)

____ 4. Identify the range of this relation.

1

3

6

8

9

–2

0

3

5

a. c.

b. d.


____ 5. This graph shows the height of the tide in a harbour as a function of time in one day. What is the greatest height of the tide?

Time (24-h clock)

Hei

gh

t (m

)

Height of the Tide in a Harbour

03:00 06:00 09:00 12:00 15:00 18:00 21:00 24:0000:000

2

4

6

8

10

a. 9 m b. 2 m c. 8 m d. 4 m

____ 6. Each point on this graph represents a person. Which two people are the same age?

AB

C D

E

F

G

Age (years)

Mas

s (k

g)

Ages and Masses of People

0 4 8 12 16 20

20

40

60

80

a. E and F c. D and E

b. C and D d. B and C


____ 7. Which graph best represents the cost of renting a kayak as a function of time?

a.

Time (h)

Co

st (

$)

Renting a Kayak

c.

Time (h)

Co

st (

$)

Renting a Kayak

b.

Time (h)

Co

st (

$)

Renting a Kayak

d.

Time (h)

Co

st (

$)

Renting a Kayak

____ 8. Which set of ordered pairs does not represent a function?

a)

b)

c)

d)


____ 9. Which of these graphs represents a function?

a) b)

x

y

x

y

c) d)

x

y

x

y


____ 10. Which of these graphs represents a function?

a) b)

x

y

x

y

c) d)

x

y

x

y

____ 11. This set of ordered pairs represents a linear relation. Determine its rate of change.

a. 3

7c. 7

3

b. 7

3d.

37


____ 12. The monthly income, I dollars, of a furniture salesperson is given by the equation , where s represents the salesperson’s total monthly sales in dollars. Determine the rate of change of this linear relation.

a. 0.03 c. 1500

b. 33.3 d. 3

____ 13. Which graph represents the linear function ?

a.

0 2 4–2–4 x

2

4

–2

–4

yc.

0 2 4–2–4 x

2

4

–2

–4

y

b.

0 2 4–2–4 x

2

4

–2

–4

yd.

0 2 4–2–4 x

2

4

–2

–4

y


Written Answers: Show all necessary work.

14. a) Write in function notation:

b) Write as an equation in two variables:

15. This graph shows the volume of gas in a car as a function of time. Describe what is happening for line segment EF in the graph.

Time from start of journey (h)

Vo

lum

e o

f g

as (

L)

Volume of Gas in a Car

A

B

C

D

E F

G

0 2 4 6 8 10 12

20

40

60

80

16. Suppose a student drew a graph of each function described below. For which graphs should the student connect the points? Justify your answer.

a) The mass of a stack of coins is a function of the number of coins.

b) The temperature in Vancouver is a function of the time of day.

c) The mass of an animal is a function of its age.

d) The price of a carton of milk is a function of the size of the carton.


17. This is a graph of the function .

h(x) = –1/2x + 1

0 2 4–2–4 x

2

4

–2

–4

y

a) Determine the range value when the domain value is –2.

b) Determine the domain value when the range value is –1.

18. Determine the domain and range of the graph of this function. Write in set and interval notation.

y = f(x)0 2 4–2–4 x

2

4

–2

–4

–6

y

19. Which equations represent linear relations? Create tables of values if necessary.

a) b)

c) d)


20. This table represents the approximate relation between a distance in miles and the same distance in kilometres. Determine the rate of change of the relation.

Miles (mi.) 9 18 27 36 45Kilometres (km) 14.4 28.8 43.2 57.6 72.0

21. Determine the vertical and horizontal intercepts of this graph. What do they each represent?

0

y = f(x)

2 4–2–4 x

2

4

–2

–4

y

22. This graph shows the cost, C dollars, of printing an advertising flyer for the school play as a function of the number of flyers printed, n. What is the cost when 1000 flyers are printed?

Number of flyers (100s)

Co

st (

$)

Flyers for the School Play

0 4 8 12 16 20 n

100

200

300

400

500 C


23. This graph shows cost, C dollars, as a function of time, t hours. What is the time when the cost is $35?

Time (h)

Co

st (

$)

0

C = f(t)

1 2 3 4 t

10

20

30

40

50

60

C

24. The equation represents the total cost, C dollars, for a sports banquet when g people attend.

a) Write the function in function notation.

b) Determine C(46).

c) Determine the value of g when C(g) = 1581.


25. This graph represents a day trip from Vancouver to Hope, B.C. The distance between Vancouver and Hope is approximately 150 km.

Describe the journey for each segment of the graph.

Time (h)

Dis

tan

ce (

km)

Day Trip from Vancouver to Hope

O

A

B

C D

E F

G

1 2 3 4 5 6 7

15

30

45

60

75

90

105

120

135

150

165

180


26. A company rents paddle boats by the day. This table shows the total cost of renting a paddle boat for different numbers of days.

Number of Days (n)

Total Cost ($)

1 $54.003 $112.005 $170.007 $228.00

a) Graph the relation between the total cost of the rental and the number of days.

b) Does the graph represent a linear relation? How do you know?

c) Determine the rate of change, then describe what it represents.


27. This graph shows the length, l metres, of an object’s shadow as a function of the height of the object, h metres.

Height of object (m)

Len

gth

of

shad

ow

(m

)

Length of an Object's Shadow

04 8 12 16 20 24 28 32 36 h

10

20

30

40

50

60

70l

a) What is the rate of change? What does it represent?

b) A tree has height 13 m. About how long is its shadow?

c) The length of the shadow of a building is 45 m. About how tall is the building?


28. Sketch a graph of the linear function .

Education

Test 1