ALG. 2 CH. 2 TEST REVIEW - FUNCTIONS, EQUATIONS, AND GRAPHS
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Write the ordered pairs for the relation. Find the domain and range.
y
4
2
–4
–2
O
2
x
4
–2
–4
____
a. {(–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {–2, –1, 0, 1, 2}; range: {1, 2, 5}
b. {(5, –2), (2, –1), (1, 0), (2, 1), (5, 2)}; domain: {–2, –1, 0, 1, 2}; range: {1, 2, 5}
c. {(–2, 5), (–1, 2), (0, 1), (1, 2), (2, 5)}; domain: {1, 2, 5}; range: {–2, –1, 0, 1, 2}
d. {(5, –2), (2, –1), (1, 0), (2, 1), (5, 2)}; domain: {1, 2, 5}; range: {–2, –1, 0, 1, 2}
2. Graph the relation. Find the domain and range.
a.
c.
y
y
2
–2
2
2
–2
x
–2
2
–2
domain:
domain:
range:
range:
x
b.
d.
y
y
2
–2
2
2
–2
x
–2
____
x
–2
domain:
domain:
range:
range:
3. Make a mapping diagram for the relation.
{(–3, –2), (–1, 1), (2, 2), (4, 4)}
a.
c.
–3
4
–3
–2
–1
2
–1
1
2
1
2
2
4
–2
4
4
b.
____
2
d.
–3
–1
–3
–2
–2
1
–1
1
2
4
2
2
2
4
4
4
4. Find the domain and range of the relation and determine whether it is a function.
y
4
2
–4
–2
O
2
x
4
–2
–4
____
a. Domain: all real numbers; range: all real numbers; yes, it is a function
b. Domain: x > 0; range: y > 0; yes, it is a function.
c. Domain: positive integers; range: positive integers; no, it is not a function.
d. Domain: x  0; range: y  0; no, it is not a function.
5. Use the vertical-line test to determine which graph represents a function.
y
y
a.
c.
–4
–2
4
4
2
2
O
4
–2
6. Graph the equation
–2
O
–2
–4
–4
d.
y
–4
–4
x
–2
b.
____
2
4
2
2
2
4
x
–4
–2
O
–2
–2
–4
–4
.
4
x
2
4
x
y
4
O
2
a.
–4
–2
4
2
2
O
2
4
–2
–4
x
–2
O
–2
–2
–4
–4
d.
y
–4
y
4
b.
____
c.
y
4
2
2
2
4
x
–4
–2
O
–2
–2
–4
–4
7. Graph the equation
a.
16
4
x
2
4
x
12
16
x
y
4
O
2
by finding the intercepts.
y
c.
y
4
12
O
8
–4
4
–8
–16
–12
–8
–4
O
4
x
–12
–4
–16
4
8
b.
16
–4
d.
y
16
12
12
8
8
4
4
O
4
8
12
–4
x
–4
O
y
4
8
12
16 x
–4
Find the slope of the line through the pair of points.
____
8.
y
8
4
–8
–4
O
4
8
x
–4
–8
a.
b. 4
c. 3
d.
4
3

3
3
4
4
____ 9. (11, –8) and (–4, –4)
a.
b.
c. 15
d. 4
15
4


4
15
4
15
____ 10. Find the point-slope form of the equation of the line passing through the points (4, 8) and (–4, 0).
a. y – 8 = (x – 4)
c. y – 8 = (x + 4)
b. y – 0 = (x – 4)
d. y – 8 = (x – 4)

Find the slope of the line.
____ 11.
a.
3
5
b.

3
5
c. 9
d. none of these
____ 12.
y
4
2
–4
–2
O
2
4
x
–2
–4
a. 1
____ 13. y = a
a. undefined
b. 0
c. –2
d. 2
b. a
c. 1
d. 0
Find an equation for the line:
5
____ 14. through (7, –2) and perpendicular to y =  x – 3.
4
a.
b.
c.
4
18
5
27
4
y= x
y= x
y= x
5
5
4
4
5
5
____ 15. through (–7, 1) and parallel to y = x + 4.
4
a.
b.
c.
4
33
4
23
5
y= x
y= x
y= x
5
5
5
5
4
____ 16. through (2, 4) and horizontal.
a. x = 4
b. y = 4
c. y = 2
38
5
d.
39
4
d.
y=
5
43
x
4
4
5
31
y= x
4
4
d. x = 2
Determine whether y varies directly with x. If so, find the constant of variation k and write the
equation.
____ 17.
x
y
4
20
24
120
144
720
864
4320
a. yes; k = 5; y =5x
b. yes; k = 6; y =6x
c. yes; k = 4; y =4x
d. no
Determine whether y varies directly with x. If so, find the constant of variation k.
____ 18. 4y = 6x
a.
b.
c. yes; 6
d. no
3
2
yes;
yes;
2
3
____ 19. The range of a car is the distance R in miles that a car can travel on a full tank of gas. The range varies
directly with the capacity of the gas tank C in gallons.
a. Find the constant of variation for a car whose range is 288 mi with a gas tank that holds
18 gal.
b. Write an equation to model the relationship between the range and the capacity of the
gas tank.
a. 16 mi/gal; R = 16C
b. 16 mi/gal; C = 16R
c.
1
1
mi/gal; R = C
16
16
d. 5184 mi/gal; RC = 5184
Find the value of y for a given value of x, if y varies directly with x.
____ 20. If y = 304 when x = 76, what is y when x = 23?
a. 92
b. 5.8
c. –92
d. –5.8
____ 21. If y = 1.8 when x = 3.6, what is y when x = 5.1?
a. –2.55
b. –10.2
c. 2.55
d. 10.2
____ 22. The distance traveled at a constant speed is directly proportional to the time of travel. If Olivia traveled 120
miles in 7.5 hours, how many miles will Olivia travel in 1.8 hours at the same constant speed?
a. 110.7 mi
b. 28.8 mi
c. 91.2 mi
d. 129.3 mi
____ 23. A 2-mi cab ride costs $2.50. A 7-mi cab ride costs $6.50. Find a linear equation that models cost c as a
function of distance d.
a. c = 0.93d + 0.90
c. d = 0.80c + 4.00
b. c = 1.25d + 4.00
d. c = 0.80d + 0.90
____ 24. A candle is 10 in. tall after burning for 2 hours. After 3 hours, it is
a.
b.
Write a linear equation to model the height h of the candle after burning t hours.
Predict how tall the candle will be after burning 6 hours.
a.
b.
Graph the absolute value equation.
____ 25.
in. tall.
c.
d.
a.
c.
y
y
8
16
4
12
8
–8
–4
O
4
8
x
4
8
x
4
8
x
–4
4
–8
–8
–4
O
4
8
x
–12
–4
b.
d.
y
–8
–4
y
16
16
12
12
8
8
4
4
O
4
8
–8
x
–4
–4
O
–4
____ 26.
a.
c.
y
4
y
4
–8
–8
–4
O
–4
–8
–12
4
8
x
–4
O
–4
–8
–12
–16
b.
4
–8
–4
O
d.
y
y
12
4
8
8
x
–4
4
–8
–8
–4
–12
–4
–16
–8
____ 27. Write two linear equations you can use to graph
a.
c.
b.
d.
____ 28. Write two linear equations you can use to graph the equation.
a.
c.
b.
d.
____ 29. Write the equation for the translation of
O
.
.
4
8
x
y
6
4
2
–6
–4
–2 O
–2
2
4
6
x
–4
–6
a.
b.
c.
d.
____ 30. Graph the equation of y = |x| translated 5 units down.
y
a.
c.
–6
–4
6
6
4
4
2
2
–2 O
–2
2
4
6
–4
–2 O
–2
–4
–6
–6
d.
y
–4
–6
x
–4
b.
–6
y
6
4
4
2
2
2
4
6
x
4
6
x
2
4
6
x
y
6
–2 O
–2
2
–6
–4
–2 O
–2
–4
–4
–6
–6
____ 31. The equation
describes a function that is translated from a parent function.
a. Write the equation of the parent function. Then find the number of units and the
direction of translation.
b. Sketch the graphs of the two functions.
a.
c.
; 6 units up;
; 6 units down;
y
–6
b.
–4
–2
y
6
6
4
4
2
2
O
2
4
6
x
–6
–4
O
–2
–2
–2
–4
–4
–6
–6
d.
; 6 units down;
–4
–2
6
4
4
2
2
2
4
6
x
–6
–4
–2
O
–2
–2
–4
–4
–6
–6
Write an equation for the vertical translation.
____ 32.
; 27 units down
a.
b.
6
x
2
4
6
x
y
6
O
4
; 6 units up;
y
–6
2
c.
____ 33. Write an equation for the horizontal translation of
d.
.
y
8
4
–8
–4
O
4
8
x
–4
–8
a.
b.
c.
____ 34. Write the equation that is the translation of
a.
b.
c.
d.
____ 35. Graph the function
a.
c.
–6
–3
right 12 units and up 2 units.
.
y
6
3
3
O
3
6
–6
x
–3
O
–3
–3
–6
–6
d.
y
–3
y
6
b.
–6
d.
6
3
3
3
6
x
6
x
3
6
x
y
6
O
3
–6
–3
O
–3
–3
–6
–6
Graph the inequality.
____ 36. x – y  –9
a.
–6
c.
y
–4
6
6
4
4
2
2
–2 O
–2
2
4
6
–4
–2 O
–2
–4
–6
–6
d.
y
–4
–6
x
–4
b.
–6
y
6
4
4
2
2
2
4
6
x
4
6
x
2
4
6
x
y
6
–2 O
–2
2
–6
–4
–2 O
–2
–4
–4
–6
–6
____ 37. A doctor’s office schedules 15-minute appointments and half-hour appointments for weekdays. The doctor
limits these appointments to, at most, 30 hours per week. Write an inequality to represent the number of 15minute appointments x and the number of half-hour appointments y the doctor may have in a week.
a.
c.
b.
d.
____ 38. Write an inequality for the graph.
y
6
3
–6
O
–3
3
6
x
–3
–6
a. 4x + 6y  24
b. 4x + 6y  24
c. 6x + 4y  24
d. 6x + 4y  24
Graph the absolute value inequality.
____ 39. y  |x + 4| + 2
a.
–6
c.
y
–3
6
6
3
3
O
3
6
–3
O
–3
–6
–6
d.
y
–3
–6
x
–3
b.
–6
y
6
3
3
3
6
x
6
x
3
6
x
y
6
O
3
–6
–3
O
–3
–3
–6
–6
Write an inequality for the graph.
____ 40.
y
6
3
–6
–3
O
3
6
x
–3
–6
a. y  |x – 5| – 2
b. y  |x + 5| – 2
____ 41. Graph the function
a.
–6
–3
c. y  |x – 5| + 2
d. y  |x – 5| – 2
.
c.
y
6
6
3
3
O
3
6
–3
O
–3
–6
–6
d.
y
–3
–6
x
–3
b.
–6
y
6
3
3
3
6
x
6
x
3
6
x
y
6
O
3
–6
–3
O
–3
–3
–6
–6
Short Answer
42. Graph the relation.
43. Is the relation {(1, –1), (0, 0), (1, 0), (0, –5), (–3, 3)} a function? Explain.
44. Is the relation {(–3, –2), (4, 3), (–1, 1), (3, –5), (0, –2)} a function? Explain.
45. For
,
.
46. What is the vertex of the function
?
Write in standard form an equation of the line passing through the given point with the given slope.
47. slope = 5; (–1, 4)
Other
48. Explain how to find the x-coordinate of the vertex of
.
49. Do the values in the table represent a direct variation? Explain your answer.
x
4
5
7
y
13.1
16.3
22.6
ALG. 2 CH. 2 TEST REVIEW - FUNCTIONS, EQUATIONS, AND GRAPHS
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
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A
A
D
B
C
B
D
B
B
D
A
D
D
C
C
B
A
A
A
A
C
B
D
B
D
C
B
B
A
B
D
C
A
D
D
A
B
B
C
A
A
SHORT ANSWER
42. ANS:
y
6
4
2
–6
–4
–2
O
2
4
6
x
–2
–4
–6
43. ANS:
No; a domain value corresponds to two or more range values.
44. ANS:
Yes; for each element in the domain there is exactly one element in the range.
45. ANS:
–17
46. ANS:
5
( , 2)
3
47. ANS:
–5x + y = 9
OTHER
48. ANS:
is in the form of
x-coordinate of the vertex is
. Find the x-coordinate of the vertex by substituting into
or 2.
49. ANS:
No; there is no constant of variation k such that
.
. The