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.
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. /domain:
range: / c. /
domain:
range:
b. /
domain:
range: / d. /
domain:
range:
____3.Make a mapping diagram for the relation.
{(–3, –2), (–1, 1), (2, 2), (4, 4)}
a. / / c. /b. / / d. /
____4.Find the domain and range of the relation and determine whether it is a function.
a. / Domain: all real numbers; range: all real numbers; yes, it is a functionb. / 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.
a. / / c. /b. / / d. /
____6.Graph the equation .
a. / / c. /b. / / d. /
____7.Graph the equation by finding the intercepts.
a. / / c. /b. / / d. /
Find the slope of the line through the pair of points.
____8.
a. / / b. / / c. / / d. /____9.(11, –8) and (–4, –4)
a. / / b. / / c. / / d. /____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. / / b. / / c. / 9 / d. / none of these____12.
a. / 1 / b. / 0 / c. / –2 / d. / 2____13.y = a
a. / undefined / b. / a / c. / 1 / d. / 0Find an equation for the line:
____14.through (7, –2) and perpendicular to y = x – 3.
a. / y = x / b. / y = x / c. / y = x / d. / y = x____15.through (–7, 1) and parallel to y = x + 4.
a. / y = x / b. / y = x / c. / y = x / d. / y = x____16.through (2, 4) and horizontal.
a. / x = 4 / b. / y = 4 / c. / y = 2 / d. / x = 2Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
____17.
x / y4 / 20
24 / 120
144 / 720
864 / 4320
a. / yes; k = 5; y =5x / c. / yes; k = 4; y =4x
b. / yes; k = 6; y =6x / d. / no
Determine whether y varies directly with x. If so, find the constant of variation k.
____18.4y = 6x
a. / yes; / b. / yes; / c. / yes; 6 / d. / no____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 18gal.b. / Write an equation to model the relationship between the range and the capacity of the gas tank.
a. / mi/gal; R = C / c. / mi/gal; R = C
b. / mi/gal; C = R / 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 + 4.00b. / 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 in. tall.
a. / Write a linear equation to model the height h of the candle after burning t hours.b. / Predict how tall the candle will be after burning 6 hours.
a. / / c. /
b. / / d. /
Graph the absolute value equation.
____25.
a. / / c. /b. / / d. /
____26.
a. / / c. /b. / / d. /
____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 .
a. / / b. / / c. / / d. /____30.Graph the equation of y = |x| translated 5 units down.
a. / / c. /b. / / d. /
____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. / ; 6 units up;
/ c. / ; 6 units down;
b. / ; 6 units down;
/ d. / ; 6 units up;
Write an equation for the vertical translation.
____32.; 27 units down
a. / / b. / / c. / / d. /____33.Write an equation for the horizontal translation of .
a. / / b. / / c. / / d. /____34.Write the equation that is the translation of right 12 units and up 2 units.
a. / / c. /b. / / d. /
____35.Graph the function .
a. / / c. /b. / / d. /
Graph the inequality.
____36.x – y –9
a. / / c. /b. / / d. /
____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 15-minute 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.
a. / 4x + 6y 24 / c. / 6x + 4y 24b. / 4x + 6y 24 / d. / 6x + 4y 24
Graph the absolute value inequality.
____39.y |x + 4| + 2
a. / / c. /b. / / d. /
Write an inequality for the graph.
____40.
a. / y |x – 5| – 2 / c. / y |x – 5| + 2b. / y |x + 5| – 2 / d. / y |x – 5| – 2
____41.Graph the function .
a. / / c. /b. / / d. /
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 / 7y / 13.1 / 16.3 / 22.6
ALG. 2 CH. 2 TEST REVIEW - FUNCTIONS, EQUATIONS, AND GRAPHS
Answer Section
MULTIPLE CHOICE
1.ANS:A
2.ANS:A
3.ANS:D
4.ANS:B
5.ANS:C
6.ANS:B
7.ANS:D
8.ANS:B
9.ANS:B
10.ANS:D
11.ANS:A
12.ANS:D
13.ANS:D
14.ANS:C
15.ANS:C
16.ANS:B
17.ANS:A
18.ANS:A
19.ANS:A
20.ANS:A
21.ANS:C
22.ANS:B
23.ANS:D
24.ANS:B
25.ANS:D
26.ANS:C
27.ANS:B
28.ANS:B
29.ANS:A
30.ANS:B
31.ANS:D
32.ANS:C
33.ANS:A
34.ANS:D
35.ANS:D
36.ANS:A
37.ANS:B
38.ANS:B
39.ANS:C
40.ANS:A
41.ANS:A
SHORT ANSWER
42.ANS:
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:
(, 2)
47.ANS:
–5x + y = 9
OTHER
48.ANS:
is in the form of . Find the x-coordinate of the vertex by substituting into . The x-coordinate of the vertex is or 2.
49.ANS:
No; there is no constant of variation k such that .