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2-8 Graphing Linear and Absolute Value Inequalities
Graph each inequality.
9. SOLUTION: The boundary of the graph is the graph of
Test the point (0, 0).
. Since the inequality symbol is ≥, the boundary line is solid.
The region that contains (0, 0) is shaded.
11. SOLUTION: The boundary of the graph is the graph of
Test the point (0, 0).
. Since the inequality symbol is >, the boundary line is dashed.
The region that does not contain (0, 0) is shaded.
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13. Page 1
2-8 Graphing
Linear and Absolute Value Inequalities
11. SOLUTION: The boundary of the graph is the graph of
Test the point (0, 0).
. Since the inequality symbol is >, the boundary line is dashed.
The region that does not contain (0, 0) is shaded.
13. SOLUTION: The boundary of the graph is the graph of
. Since the inequality symbol is ≥, the boundary line is solid.
Test the point (0, 0).
The region that does not contain (0, 0) is shaded.
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2-8 Graphing Linear and Absolute Value Inequalities
13. SOLUTION: . Since the inequality symbol is ≥, the boundary line is solid.
The boundary of the graph is the graph of
Test the point (0, 0).
The region that does not contain (0, 0) is shaded.
Graph each inequality.
15. SOLUTION: The boundary of the graph is the graph of
.
This is a horizontal compression of the absolute value graph
Since the inequality symbol is >, the boundary line is dashed.
Test the point (0, 0).
.
The region that does not contain (0, 0) is shaded.
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2-8 Graphing Linear and Absolute Value Inequalities
Graph each inequality.
15. SOLUTION: The boundary of the graph is the graph of
.
This is a horizontal compression of the absolute value graph
Since the inequality symbol is >, the boundary line is dashed.
Test the point (0, 0).
.
The region that does not contain (0, 0) is shaded.
17. SOLUTION: The related equation can be written
.
The negative sign reflects the absolute value graph
across the y-axis (which has no effect, since it is
symmetric). The 2 compresses the graph horizontally. The 6 translates the graph up 6 units.
The boundary of the graph is the graph of
Test the point (0, 0).
. Since the inequality symbol is <, the boundary line is dashed.
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2-8 Graphing
Linear and Absolute Value Inequalities
17. SOLUTION: The related equation can be written
.
The negative sign reflects the absolute value graph
across the y-axis (which has no effect, since it is
symmetric). The 2 compresses the graph horizontally. The 6 translates the graph up 6 units.
The boundary of the graph is the graph of
Test the point (0, 0).
. Since the inequality symbol is <, the boundary line is dashed.
The region that contains (0, 0) is shaded.
19. SOLUTION: The related equation can be written
.
The –5 translates the graph of
5 units to the right. The 4 compresses the graph horizontally. The compresses the graph vertically.
The boundary of the graph is the graph of
. Since the inequality symbol is >, the boundary line is dashed.
Test the point (0, 0).
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2-8 Graphing Linear and Absolute Value Inequalities
19. SOLUTION: The related equation can be written
.
The –5 translates the graph of
5 units to the right. The 4 compresses the graph horizontally. The compresses the graph vertically.
The boundary of the graph is the graph of
. Since the inequality symbol is >, the boundary line is dashed.
Test the point (0, 0).
The region that does not contain (0, 0) is shaded.
21. SCHOOL DANCE Carlos estimates that he will need to earn at least $700 to take his girlfriend to the prom. Carlos
works two jobs as shown in the table.
a. Write an inequality to represent this
situation.
b. Graph the inequality.
c. Will he make enough working 50 hours at each job?
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SOLUTION: a. Let a be the number of hours Carlos works at Main St. Deli.
Let b be the number of hours Carlos works babysitting.
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2-8 Graphing Linear and Absolute Value Inequalities
SOLUTION: a. Let a be the number of hours Carlos works at Main St. Deli.
Let b be the number of hours Carlos works babysitting.
The inequality that represents Carlos’s earnings is
.
b. The boundary of the graph is the graph of
. Since the inequality symbol is ≥, the boundary is solid.
Test the point (0, 0).
The region that does not contain (0, 0) is shaded.
c. Substitute 50 for x and 50 for y in the inequality
.
Yes, Carlos will earn enough money if he works 50 hours at each job.
Graph each inequality.
23. SOLUTION: The boundary of the graph is the graph of
.
This is the graph of the absolute value function
translated right 3 units and up 4 units.
Since the inequality symbol is ≤, the boundary is solid.
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the point
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Yes, CarlosLinear
will earn
enough
money
if heInequalities
works 50 hours at each job.
2-8 Graphing
and
Absolute
Value
Graph each inequality.
23. SOLUTION: The boundary of the graph is the graph of
.
This is the graph of the absolute value function
translated right 3 units and up 4 units.
Since the inequality symbol is ≤, the boundary is solid.
Test the point (0, 0).
The region that contains (0, 0) is shaded.
25. SOLUTION: Graph the inequality |y| > |x|. Test various values of x and y, both negative and positive, to see if they make the
inequality true.
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SOLUTION: The absolute value of any expression is always 0 or positive. So, it is always greater than any negative number. Page 8
2-8 Graphing Linear and Absolute Value Inequalities
27. SOLUTION: The absolute value of any expression is always 0 or positive. So, it is always greater than any negative number. Therefore, this equation is true for all ordered pairs of real numbers (x, y). (The graph would be shaded
everywhere.)
39. Which of the following sets of numbers represents an infinite set?
A {2, 4, 6}
B {whole numbers between –50 and 50}
C {integers}
D
SOLUTION: The set of integers is an infinite set. So, the correct choice is C.
41. ACT/SAT For which function is the range
F G
H
J
K SOLUTION: The range of the function
So, the correct choice is K.
is Write an equation for each graph.
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SOLUTION: The range of the function
is 2-8 Graphing
Linear and Absolute Value Inequalities
So, the correct choice is K.
Write an equation for each graph.
43. SOLUTION: The given graph is a combination of transformations of the parent graph
.
When a constant k is added to or subtracted from a parent function, the result
is a translation of the graph up or down.
When a constant h is added to or subtracted from x before evaluating a parent function, the result,
translation left or right.
The graph was moved 5 units down and 4 units left.
So, the equation of the graph is
, is a
Graph each function.
45. SOLUTION: Graph each line on its domain. Use solid dots for endpoints where there is a ≤ or ≥ symbol, and an open circle where
there is a < or > symbol.
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SOLUTION: Page 10
2-8 Graphing
Linear and Absolute Value Inequalities
47. SOLUTION: Graph each line on its domain. Use solid dots for endpoints where there is a ≤ or ≥ symbol, and an open circle where
there is a < or > symbol.
Write each equation in standard form. Identify A , B, and C.
49. 12y + x = –3y + 5x – 6
SOLUTION: Rewrite the given equation in the standard form
So, A = 4, B = –15 and C = 6.
51. TENNIS Sixteen players signed up for tennis lessons. The instructor plans to use 50 tennis balls for every player and
have 200 extra. How many tennis balls are needed for the lessons?
SOLUTION: Total number of tennis balls needed for the lessons
Multiply.
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53. (6x + 5)(–x – 3)
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2-8 Graphing Linear and Absolute Value Inequalities
Multiply.
53. (6x + 5)(–x – 3)
SOLUTION: Use the FOIL method to multiply two binomials.
Graph each linear equation.
55. y = 2x – 8
SOLUTION: Graph a line with slope 2 and y-intercept –8.
57. 3y – 4x = 24
SOLUTION: Graph the equation 3y – 4x = 24. The y-intercept is 8 and the x-intercept is –6.
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