Name:_______________________________________________Period:_____
Date:_______________________________________
Advanced Algebra II
Ch. 2 Homework Packet
Section 2.1 – Relations and Functions
1. The table shows the number of gold medals won by the United States athletes during the Summer
Olympics. Represent the data using each of the following:
a) A mapping diagram
b) Ordered pairs
c) A graph on the coordinate plane
Determine whether each relation is a function.
2.
3.
4. Using the vertical line test to determine whether the graph represents a function.
Evaluate each function for the given value of x, and write the input x and the output f (x) as an ordered pair.
9
5. f(x) = 3x + 2 for x = 3
6. f(x) = 5x  22 for x = 12
7. 𝑓(𝑥) = 4 𝑥 − 15 𝑓𝑜𝑟 𝑥 = 4
8. Write a function rule to model the cost of renting a truck for one day. Then evaluate the function for the
given number of miles.
Daily rental: $19.95
Rate per mile: $.50 per mile
Miles traveled: 73 miles
9. Find the domain and range of the relation, and determine whether it is a function.
Function: YES
or
No
Domain:_____________________Range:_______________________
10. The surface area of a sphere is a function of the radius of the sphere: A = 4πr2. Evaluate the function
for a basketball with a radius of 11.5 cm.
Section 2.2 – Direct Variation
For each function, determine whether y varies directly with x. If so, find the constant of variation and write
the function rule.
11.
12.
Determine whether y varies directly with x. If so, find the constant of variation.
13. y = 1.2x
14. y  3x = 1
15. y + 2 = x
For questions 16 and 17, y varies directly with x.
16. If y = 14 when x = 7, find x when y = 22.
17. If y = 4 when x = 14, find y when x = 5.
18. The amount of lemon juice in a lemonade recipe varies directly with the amount of water. The recipe
calls for 8 oz of lemon juice and 32 oz of water. How much lemon juice should you use if you start with 28
oz of water?
Make a table of x- and y-values and use it to graph the direct variation equation.
1
19. 𝑦 = 5 𝑥
Write and graph a direct variation equation that passes through each point.
3
7
20. (-1.5, 9)
21. (7, 3)
22. (5 , − 2)
23. (3, 165)
5
24. Y varies directly with x. If 𝑦 = 17 when x = 10, find y when x = 5.
25. A new hybrid car has a 12-gallon gas tank. On one tank of gas, the owner can drive 540 miles. The
number of miles traveled varies directly with the number of gallons of gas the car uses.
A. Write an equation that relates the number of miles traveled with the number of gallons of gas
used.
B. How many miles can the owner travel on 9 gallons of gas?
Section 2.3 – Linear Functions and Slope-Intercept Form
Find the slope of the line through each pair of points.
26. (0, 1) and (3, 0)
27. (3, 2) and (1, 6)
28. (3, 5) and (1, 2)
29. (3, 3) and (1, 3)
Write an equation for each line.
30. m = 4 and the y-intercept is 3.
31. m = 0 and the y-intercept is 4.
32. Find the slope and y-intercept of the line.
Find the slope and y-intercept of each line.
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33. 3x  4y = 12
34. 𝑓(𝑥) = 4 𝑥 + 7
Graph each equation.
36. 4x + 3y = 12
35. 4x  3y = 6
3
1
37. 𝑦 = − 2 𝑥 + 2
38. Find the slope and y-intercept of the line.
39. The equation e = 1200 + 11t represents your elevation e in feet for each minute t you hike from a
trailhead.
A. If you graphed this equation, what would the slope represent? Explain.
B. Are you hiking uphill or downhill? Explain.
Section 2.4 – More About Linear Equations
Write an equation of each line.
40. slope = 2; (2, 1)
41. Slope = 0; (-2, 3)
Write in point-slope form an equation of the line through each pair of points.
43. (-2, 3) and (2, 9)
44. (-2, -3) and (2, -1)
45. (-12, 20) and (-21, 29)
5
42. Slope = 9; (10, 4)
Write an equation of each line in standard form with integer coefficients.
3
1
46. 𝑦 = 2 𝑥 − 2
47. y = 4.2x + 1.8
48. Find the intercepts and graph each line.
49. Write and graph an equation to represent the situation. You have a $30 gift card to an online music
store. The gift card will allow you to purchase 5 albums.
Write an equation of the line through each point. Use slope-intercept form.
50. through (7, 1) and perpendicular to y = -x + 3
51. through (3, 1) and perpendicular to -4x + y – 1 = 0
52. Graph the equation.
3x + y = 4
53.
A. Graph y = 3x + 2
B. Write an equation of the line parallel to the line in part (a) passing through the point (2, 0).
Graph the line on the same set of axes.
C. Write an equation of the line perpendicular to the line in part (a) passing through the point
(0, 4). Graph the line on the same set of axes.
D. What is the relationship between the lines from part (b) and part (c)?
Section 2.5 – Using Linear Models
54. Make a scatter plot and describe the correlation.
Write the equation of a trend line, if possible, for questions 55 and 56.
55. {(1, 2.1), (3, 3.1), (5, 4.0), (7, 5.2), (9, 5.9)}
56. The table shows the number of misdirected bags and the number of late flight
arrivals by week, for one airline.
57. The table shows the percent of the population not covered by health insurance in selected states for
the years 1997 and 2006.
A. Which variable should be the independent variable?
B. Make a scatter plot. Use a calculator to find the line of best fit.
C. In Wyoming, 15.5% of the population was not covered by health insurance in 1997. Use the
equation from part (c) to predict the percent of the population that was not covered in 2006.
D. The actual percent for Wyoming in 2006 was 14.6%. Is the line of best fit accurate? Explain.
58. The table shows the price per box of fresh Florida oranges from 2001 to 2006.
A. Make a scatter plot and find the trend line. Let x = the number of years since 2000.
B. In 2007, the price per box of fresh oranges was $16. Does this information follow the trend?
Explain.
C. Is a model invalid if new data does not fit its predictions? Explain.
Section 2.6 – Families of Functions
59. How is the function related to y = x? Graph the function by translating the parent function.
y=x+2
Make a table of values for f(x) after the given translation.
60. 2 units down
61. 1 unit down
62. Write an equation for the vertical translation of y = f(x).
5 units up
63. For the function, identify the horizontal translation ofg the parent function f(x) = x2. Then graph the
function.
Y = (x + 1.8)2
64. The graph of the function f (x) is shown at the right.
A. Make a table of values for f (x) and f (x)  2.
B. Graph f (x) and f (x)  2 on the same coordinate grid.
65. Write an equation for the transformation of y = x.
Vertical stretch by a factor of 3
66. Describe the transformations of f(x) that produce g(x).
𝑥
f(x) = 4x; g(x) = − 1
2
67. Write the equations for f(x) and g(x). Then identify the reflection that transforms the graph of f(x) to
the graph of g(x).
68. Graph each pair of functions on the same coordinate plane. Describe a transformation that changes
f(x) to g(x).
Section 2.7 – Absolute Value Functions and Graphs
Graph each equation. Try without using calculator
69. y = |x| - 2
70. y = |x| - 5
71. y = |x – 3| + 1
Graph each equation. Then describe the transformation from the parent function f(x) = |x|.
72. y = 2|x|
73. y = -3|x|
Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function f(x)
= |x|.
74. y = -3|x| - 2
75. y = 5 - |x – 1|
Graph each absolute value equation.
76. y = |3 – x|
77. y = -|-x – 2|
78. y = |3x – 1| - 2
1
79. 𝑦 = 3 |2𝑥 − 9|
1
80. 𝑦 = − 2 |2𝑥 − 4|
Section 2.8 – Two-Variable Inequalities
Graph each inequality.
82. y < x
83. y > 2
84. 𝑥 ≤ 2
85. −2𝑦 ≤ −𝑥 − 2
86. You have a $25 calling card. Calls made using the card within the United States cost $.10 per minute
while calls made from the US to France cost $.25 per minute.
A. Write an inequality that relates the number of minutes x you can use for calls within the U.S.
and the number of minutes y you can use for calls from the U.S. to France.
B. Graph the inequality.
Graph each absolute value inequality.
87. y > |x + 2|
88. y > |x| + 2
88. Write an inequality for the graph. The equation for the boundary line is given.
-2x – 3y = 6
Graph each inequality on a coordinate plane.
89. 4x + 2y < 8
1
90. 𝑦 > − 6 𝑥 − 1
Write an inequality for each graph.
91.
92.
93.
94. Write an inequality that includes (0, 9), (-10, 10), (10, -20), and (-20, 15) as solutions.