Download Simplify each expression. 12. SOLUTION: 14. SOLUTION: 16

Study Guide and Review - Chapter 8
2
Simplify each expression.
16. GEOMETRY A triangle has an area of 3x + 9x –
54 square centimeters. If the height of the triangle is
x + 6 centimeters, find the length of the base.
12. SOLUTION: Let b = length of the base of the triangle.
SOLUTION: The length of the base of the triangle is
centimeters.
14. SOLUTION: Simplify each expression.
18. SOLUTION: 2
16. GEOMETRY A triangle has an area of 3x + 9x –
54 square centimeters. If the height of the triangle is
x + 6 centimeters, find the length of the base.
SOLUTION: Let b = length of the base of the triangle.
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The length of the base of the triangle is
centimeters.
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Study
Guide and Review - Chapter 8
Graph each function. State the domain and
range.
20. 24. SOLUTION: SOLUTION: The graph of
represents a transformation of the graph of
.
a = –12: The graph is expanded and is reflected
across the x-axis.
k = 2: The graph is translated 2 units up. There is an
asymptote at f (x) = 2.
22. SOLUTION: Graph each function. State the domain and
range.
26. 24. SOLUTION: SOLUTION: The graph of
The graph of
represents a transformation of the graph of
.
represents a transformation of the graph of
.
a = 3: The graph is expanded.
a = –12: The graph is expanded and is reflected
across the x-axis.
h = −5: The graph is translated 5 units left. There is
an asymptote at x = −5.
k = 2: The graph is translated 2 units up. There is an
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asymptote at f (x) = 2.
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Guide and Review - Chapter 8
26. 28. SOLUTION: SOLUTION: The graph of
represents a transformation of the graph of
.
represents a The graph of
transformation of the graph of
.
a = 3: The graph is expanded.
a = 7: The graph is expanded.
h = −5: The graph is translated 5 units left. There is
an asymptote at x = −5.
h = 2: The graph is translated 2 units right. There is
an asymptote at x = 2.
k = 3: The graph is translated 3 units up. There is an
asymptote at
.
.
28. SOLUTION: The graph of
transformation of the graph of
represents a .
30. CONSERVATION The student council is planting
28 trees for a service project. The number of trees
each person plants depends on the number of student
council members.
a. Write a function to represent this situation.
a = 7: The graph is expanded.
b. Graph the function.
h = 2: The graph is translated 2 units right. There is
an asymptote at x = 2.
SOLUTION: a. Let x be the number of student council members.
k = 3: The graph is translated 3 units up. There is an
asymptote at
.
The function representing the situation is
b. The graph of
.
represents a eSolutions Manual - Powered by Cognero
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transformation of the graph of
.
Study Guide and Review - Chapter 8 .
Determine the equations of any vertical
asymptotes and the values of x for any holes in
the graph of each rational function.
30. CONSERVATION The student council is planting
28 trees for a service project. The number of trees
each person plants depends on the number of student
council members.
32. a. Write a function to represent this situation.
b. Graph the function.
SOLUTION: SOLUTION: a. Let x be the number of student council members.
The function representing the situation is
.
b. The graph of
represents a transformation of the graph of
.
Therefore, there is a vertical asymptote at x = −4.
There is a hole at x = −2.
Here a = 28, the graph is stretched vertically.
Graph each rational function.
34. SOLUTION: There is a zero at x = −2.
Determine the equations of any vertical
asymptotes and the values of x for any holes in
the graph of each rational function.
There is a vertical asymptote at x = −5.
32. SOLUTION: Since the degree of the numerator is less than the
degree of the denominator, the horizontal asymptote
is at y = 0.
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Therefore, there is a vertical asymptote at x = −4.
There is a hole at x = −2.
Study
Guide and Review - Chapter 8
Graph each rational function.
36. 34. SOLUTION: SOLUTION: There is a zero at x = −2.
There is a vertical asymptote at x = −5.
Since the degree of the numerator is less than the
degree of the denominator, the horizontal asymptote
is at y = 0.
is same as the The graph of
graph of
with a hole at x = −2.
Draw the asymptotes, and then use a table of values
to graph the function.
39. If a varies directly as b and b = 18 when a = 27, find
a when b = 10.
SOLUTION: Substitute b = 10 in the relation
.
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40. If y varies inversely as x and y = 15 when x = 3.5,
find y when x = –5.
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SOLUTION: Study Guide and Review - Chapter 8
40. If y varies inversely as x and y = 15 when x = 3.5,
find y when x = –5.
Solve each equation or inequality. Check your
solutions.
SOLUTION: 46. SOLUTION: Substitute x = −5 in the relation
.
42. If y varies jointly as x and z, and x = 8 and z = 3
when y = 72, find y when x = –2 and z = –5.
Check:
SOLUTION: Substitute x = −2 and z = −5 in the relation y = 3xz.
The solution is x = 13.
Solve each equation or inequality. Check your
solutions.
48. SOLUTION: 46. SOLUTION: eSolutions Manual - Powered by Cognero
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48. Study
Guide and Review - Chapter 8
SOLUTION: Check: x = –4
The solution is
.
50. SOLUTION: The excluded value for this inequality is x = 1.
Check:
Solve the related equation
.
Check: x = –4
There exists no real solution for the quadratic
equation
.
Divide the real line in to two regions as shown.
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The solution is
Test x = 0.
.
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Study Guide and Review - Chapter 8
Test x = 0.
Test x = 2.
Therefore, the solution is x < 1.
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