Name: ________________________ Class: ___________________ Date: __________
ID: A
Math 10 - Unit 6 - Functions - UNIT REVIEW WORKSHEET
Multiple Choice
Identify the choice that best answers the question.
1. Which set of ordered pairs does not represent a function?
ÔÏ
Ô¸
i) ÌÔ ÊÁË 4,7 ˆ˜¯ , ÊÁË 5,10 ˆ˜¯ , ÊÁË 6,13 ˆ˜¯ , ÊÁË 4,1 ˆ˜¯ ˝Ô
Ó
˛
ÔÏ Ê ˆ Ê
Ô¸
ˆ
Ê
ˆ
Ê
ii) ÌÔ ÁË 6,8 ˜¯ , ÁË 7,−9 ˜¯ , ÁË 9,11 ˜¯ , ÁË 10,−12 ˆ˜¯ ˝Ô
Ó
˛
ÔÏ Ê
Ô¸
ˆ
Ê
ˆ
Ê
ˆ
Ê
ˆ
iii) ÌÔ ÁË −1,−10 ˜¯ , ÁË 1,−8 ˜¯ , ÁË 0,7˜¯ , ÁË 2,9 ˜¯ ˝Ô
Ó
˛
ÏÔ Ê ˆ Ê ˆ Ê
¸Ô
ˆ
Ê
ˆ
iv) ÌÔ ÁË 9,0 ˜¯ , ÁË 6,1 ˜¯ , ÁË −8,7 ˜¯ , ÁË −10,0 ˜¯ ˝Ô
Ó
˛
a. i b. ii c. iv d. iii
2. Identify the domain of this relation.
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ÌÔ ÁË 10,12 ˆ˜¯ , ÊÁË 7,9 ˆ˜¯ , ÊÁË 11,−13 ˆ˜¯ , ÊÁË 8,−10 ˆ˜¯ ˝Ô
Ó
˛
a. {−10,9,11,12} b. {−13,− 10,9,12} c. {7,8,10,11} d. {7,8,11,12}
3. This table shows the profit, P dollars, of different numbers of people attending a carnival, n. Identify the range.
Number of People,
n
1
2
3
4
5
Profit, P
($)
12.50
25.00
37.50
50.00
62.50
a. {1, 2, 3, 4, 5, ...} b. {12.50, 25.00, 37.50, 50.00, 62.50, ...}
c. {1, 2, 3, 4, 5, 12.50, 25.00, 37.50, 50.00, 62.50} d. {1, 12.50, 2, 25.00, 3, 37.50, 4, 50.00, 5, 62.50, ...}
4. For the function f (x ) = −4x + 2 , determine f(−5) .
a. 10 b. –7 c. 22 d. 0
5. For the function f (x ) = −x − 8 , determine x when f (x ) = −16 .
a. 56 b. –40 c. 8 d. –8
1
Name: ________________________
ID: A
6. Identify the independent variable and the dependent variable for this table of values.
Time,
t
4
5
9
20
30
a.
b.
independent variable: M
dependent variable: t
independent variable: domain
dependent variable: range
Money
Earned, M ($)
38.00
47.50
85.50
190.00
285.00
c.
d.
independent variable: money earned
dependent variable: time
independent variable: time
dependent variable: money earned
7. This is a graph of the function g (x ) = −3x + 2 . Determine the domain value when the range value is 2.
a. 0 b. –2.5 c. –1 d. 0
2
Name: ________________________
ID: A
8. Which of these graphs represents a function?
i)
ii)
iii)
iv)
a. ii b. i c. iii d. iv
3
Name: ________________________
ID: A
9. Which of these graphs represents a function?
i)
ii)
iii)
iv)
a. iv b. ii c. i d. iii
10. Determine the range of the graph.
a. −5 ≤ y ≤ 3 b. −3 ≤ y ≤ 3 c. −5 ≤ x ≤ 1 d. −3 ≤ y ≤ 1
11. Which of the following expressions is interval notation for a domain of 4 ≤ x < 12
a. ( 4 , 12 ) b. [ 4 , 12 ] c. ( 4 , 12 ] d. [ 4 , 12 )
4
Name: ________________________
ID: A
12. Which of the following expressions is interval notation for a domain of −6 < x ≤ −2
a. ( -6 , -2 ) b. [ -6 , -2 ] c. ( -6 , -2 ] d. [ -6 , -2 )
13. 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.
c.
b.
d.
5
Name: ________________________
ID: A
14. 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?
a. 9 m b. 2 m c. 8 m d. 4 m
6
Name: ________________________
ID: A
15. This graph shows the height of the tide in a harbour as a function of time in one day. Which statement best
describes the tide at Point C?
a. The tide is at its greatest height. b. The tide is at its least height. c. The tide is 7.1 m high. d. The tide is 4
m high.
16. This graph shows the free-fall speed of a skydiver as a function of time. Which statement best describes what is
happening for line segment BC in the graph?
a. The skydiver landed on the ground. b. The skydiver opened her parachute. c. The skydiver was
free-falling. d. The skydiver jumped out of the plane.
7
Name: ________________________
ID: A
17. Gail leaves the house for her morning jog. She stops for a quick drink, then continues jogging before stopping
again to chat with a friend. She then jogs back home. Which graph best represents Gail’s run?
8
Name: ________________________
ID: A
a.
b.
c.
d.
9
Name: ________________________
ID: A
18. The altitude of a plane, a metres, is related to the time, t minutes, that has elapsed since it started its ascent.
Determine the rate of change of this linear relation.
t (min)
a (m)
0
4000
2
5400
4
6800
6
8200
8
9600
a. 1500 m/min b. 1400 m/min c. 1200 m/min d. 700 m/min
19. Minerva has $100. This graph represents the money Minerva would have if she purchased different numbers of
CDs. Determine the rate of change of the relation.
a. $10 /CD b. −$20 /CD c. −$10 /CD d. $14.29 /CD
20. The relation between x and y is linear. Which ordered pair completes this table of values?
x
y
7
–4
4
–7
1
–10
–2 –13
a. (–5, –16) b. (–16, –5) c. (–13, –5) d. (–5, –13)
Short Answer You must clearly show your process and box your final answer.
4
21. For the function g (x ) = − x + 2 , determine x when g (x ) = 14 .
3
22. a) Write in function notation: h = x − 4
b) Write as an equation in two variables: k(x) = −2x − 7
10
Name: ________________________
ID: A
23. For the function p (x ) = 3x 2 − 1, determine x when p (x ) = 11.
24. For the functions f (x ) = 6x − 3 and g(x) = −2x + 1 determine x when f(x) = g(x) .
25. For the function t(x) = 2x 2 − 6x + 1, find t(−5a)
26. Determine the domain and range of the graph of this function.
27. State the domain and range of the following function using interval notation.
28. Which equations represent linear relations? Create tables of values if necessary.
a) 5x − y = 8
d) y = x 2 + 29x − 30
b) x 2 + y 2 = 11
c) x = 7 − 6y
e) y = x 3 + 8
f) y − 5 = 0
29. This table represents the approximate relation between a distance in miles and the same distance in kilometres.
Determine the rate of change of the relation..
Miles (mi.)
Kilometres (km)
9
14.4
18
28.8
27
43.2
11
36
57.6
45
72.0
Name: ________________________
ID: A
30. Which graphs have:
i) a negative rate of change?
ii) a positive rate of change?
iii) neither a negative nor a positive rate of change?
a)
b)
c)
d)
e)
f)
12
Name: ________________________
ID: A
Problem
31. Graph the data provided in the table of values.
a) Will you join the points? Why or why not?.
Number
of Tickets,
t
30
45
75
90
120
b) Does the graph represent a function? Explain.
Cost, C
($)
10
15
20
25
30
13
ID: A
Math 10 - Unit 6 - Functions - UNIT REVIEW WORKSHEET
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
A
C
B
C
C
D
D
D
C
B
D
C
D
C
D
B
C
D
C
A
SHORT ANSWER
21.
22.
23.
24.
-9
a) h(x) = x − 4
x = 2, -2
x = 1/2
25.
26.
27.
28.
29.
30.
50a 2 + 30a + 1
Domain: −4 ≤ x < 3 Range: −3 ≤ y < 4
Domain: [−4,3)
Range: (−3,4]
The relations in parts a, c, and f are linear.
approximately 1.6 km/mi.
i) Graphs b and d have a negative rate of change.
ii) Graphs a and e have a positive rate of change.
iii) Graphs c and f have neither a negative nor a positive rate of change.
b) k = −2x − 7
1
ID: A
PROBLEM
31. a) The points are not joined because the data are only valid for whole numbers of tickets.
b) The relation is a function because there is only one cost for each number of tickets.
2