2-8 Graphing Linear and Absolute Value Inequalities
Graph each inequality.
Graph each inequality.
11. 19. SOLUTION: The boundary of the graph is the graph of
. Since the inequality symbol is >, the
boundary line is dashed.
Test the point (0, 0).
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 region that does not contain (0, 0) is shaded.
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.
Graph each inequality.
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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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.
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Since the inequality symbol is ≤, the boundary is solid.
Test the point (0, 0).
2-8 Graphing
Linear and Absolute Value Inequalities
Graph each inequality.
25. 23. 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.
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).
27. The region that contains (0, 0) is shaded.
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.)
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.
29. GIFT CARDS Susan received a gift card from an
electronics store for $400. She wants to spend the
money on DVDs, which cost $20 each, and CDs,
which cost $15 each.
a. Let d equal the number of DVDs, and let c equal
the number of CDs. Write an inequality that shows
the possible combinations of DVDs and CDs that
Susan can purchase.
b. Graph the inequality.
c. Give three possible solutions for the number of
DVDs and CDs she can buy.
SOLUTION: eSolutions Manual - Powered by Cognero
27. a. The inequality that shows the possible number of
DVDs and CDs Susan can purchase is
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.
b. The boundary of the graph is the graph of
Therefore, this equation is true for all ordered pairs
of real numbers (x, y). (The graph would be shaded
everywhere.)
2-8 Graphing
Linear and Absolute Value Inequalities
c. Sample answers: 18 CDs and 5 DVDs, 12 CDs
and 10 DVDs, or 6 CDs and 15 DVDs.
29. GIFT CARDS Susan received a gift card from an
electronics store for $400. She wants to spend the
money on DVDs, which cost $20 each, and CDs,
which cost $15 each.
a. Let d equal the number of DVDs, and let c equal
the number of CDs. Write an inequality that shows
the possible combinations of DVDs and CDs that
Susan can purchase.
Graph each inequality.
31. SOLUTION: Graph the inequality
. The boundary line
is a transformation of the graph of
the left.
b. Graph the inequality.
2 units to c. Give three possible solutions for the number of
DVDs and CDs she can buy.
SOLUTION: a. The inequality that shows the possible number of
DVDs and CDs Susan can purchase 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).
33. OPEN ENDED Create an absolute value inequality
in which none of the possible solutions fall in the
second or third quadrant.
SOLUTION: Sample answer:
The region that contains (0, 0) is shaded.
c. Sample answers: 18 CDs and 5 DVDs, 12 CDs
and 10 DVDs, or 6 CDs and 15 DVDs.
35. ERROR ANALYSIS Paulo and Janette are
graphing
Is either of them correct? Explain your reasoning.
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Graph
each
inequality.
31. Page 3
SOLUTION: Sample answer:
2-8 Graphing
Linear and Absolute Value Inequalities
35. ERROR ANALYSIS Paulo and Janette are
graphing
Is either of them correct? Explain your reasoning.
The region that does not contain (0, 0) is to be
shaded.
37. WRITING IN MATH Describe a situation in
which there are no solutions to an absolute value
inequality. Explain your reasoning.
SOLUTION: Sample answer: One possibility is when
In order for there to be a solution, the absolute value of
y will need to be less than 0, and, by definition of
absolute value, this is impossible.
SOLUTION: Paulo’s graph is correct. Test the point (0, 0).
The region that does not contain (0, 0) is to be
shaded.
37. WRITING IN MATH Describe a situation in
which there are no solutions to an absolute value
inequality. Explain your reasoning.
SOLUTION: Sample answer: One possibility is when
In order for there to be a solution, the absolute value of
y will need to be less than 0, and, by definition of
absolute value, this is impossible.
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