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5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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Student: _____________________Date: _____________________
Instructor: Virginia DavisCourse: Foundations for College Math(1)
Assignment: Final Exam Review Ch78
Simplify the expression.
x + 3
x2 − 5x − 24
Select the correct choice below and fill in any answer boxes in your choice.
A. (Simplify your answer.)x + 3
x2 − 5x − 24=
B. The expression cannot be simplified.
Find the product and simplify if possible.
•x
11x − 55x2 − 5x
7
•x
11x − 55x2 − 5x
7=
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Find the product and simplify if possible.
•x2 − 36
x2 − 3x − 18
x + 3
x
(Simplify your answer.)•x2 − 36
x2 − 3x − 18
x + 3
x=
Find the quotient and simplify the result.
÷3w4
2w615w
4w4
÷3w4
2w615w
4w4=
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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6.
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Find the quotient and simplify the result.
÷5x5
2x425x2
4x3
÷5x5
2x425x2
4x3=
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Simplify the complex fraction.
104x58x
104x58x
=
Divide.
7x − 727
÷9x − 918
7x − 727
÷9x − 918
=
(Type an integer or a simplified fraction.)
Multiply.
•x2 + 3x
710
5x + 15
•x2 + 3x
710
5x + 15=
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Multiply.
•6x + 5y
x2 + 6xy + 9y2x + 3y
2
(Simplify your answer. Factor completely.)•6x + 5y
x2 + 6xy + 9y2x + 3y
2=
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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Find the area of the rectangle in terms of x.
feet
feet
The area of the rectangle is feet .2
(Simplify your answer.)
Add. Simplify the result if possible.
+2
5 + yy + 45 + y
(Simplify your answer.)+2
5 + yy + 45 + y
=
Subtract. Simplify the result if possible.
−5x2 + 2xx − 8
31x + 88x − 8
(Simplify your answer.)−5x2 + 2xx − 8
31x + 88x − 8
=
Subtract the rational expressions.
−12x − 6
x2 + 4x − 21
11x − 13
x2 + 4x − 21
(Simplify your answer.)−12x − 6
x2 + 4x − 21
11x − 13
x2 + 4x − 21=
Subtract the rational expressions and simplify if possible.
−− 10x2
x − 416 − 11x2
x − 4
(Simplify your answer.)−− 10x2
x − 416 − 11x2
x − 4=
2x
x2 −25
x+55x
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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Subtract the rational expressions and simplify if possible.
−7x + 3x − 3
5x + 9x − 3
(Simplify your answer.)−7x + 3x − 3
5x + 9x − 3
=
Perform the indicated operation.
+5
x
7
3x2
(Simplify your answer.)+ =5
x
7
3x2
Perform the indicated operation. Simplify if possible.
−9
x + 8
8x
x2 − 64
(Simplify your answer.)−9
x + 8
8x
x2 − 64=
Perform the indicated operation.
+ 39
x + 2
(Simplify your answer.)+ 3 =9
x + 2
Perform the indicated operation.
−4xx − 5
3xx − 3
(Simplify your answer.)−4xx − 5
3xx − 3
=
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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Find the unknown length y in the following pair of similar triangles.
15
17
23
7.5
8.5
y =
Find the unknown length y in the pair of similar triangles.
ft y = (Simplify your answer. Type an integer, fraction, or a mixed number.)
Given that the following pair of triangles are similar, find the missing length.
(Type an integer or decimal.)x =
Graph the linear equation.
f(x) = − 3x + 5
Use the graphing tool to graph the linear equation.
10 8 6 4 2 2 4 6 8 10
10
8
6
4
2
2
4
6
8
10
x
y
6 ft y
20 ft15 ft
13x
24
36
H
G
I
J
K L
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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30.
Graph the linear equation.
f(x) = x2
3
Use the graphing tool to graph the equation.
10 8 6 4 2 2 4 6 8 10
10
8
6
4
2
2
4
6
8
10
x
y
Find an equation of the line with the given slope and containing the given point. Write the equation using function
notation.
Slope ; through ( , )5 8 6
The equation of the line is f(x) .=
Find an equation of the line with the given slope and containing the given point. Write the equation using function
notation.
Slope ; through ( , )− 9 4 9
The equation of the line is f(x) . =
Find an equation of the line passing through the given points. Use function notation to write the equation.
( , ) and ( , )3 2 5 8
f(x) =
Write an equation of the line using function notation.
Horizontal; through (0, − 4)
The equation of the line is f(x) .=
Find an equation of the line. Write the equation using function notation.
Through ; perpendicular to y x(2, − 5) 5 = − 10
The equation of the line is f(x) .=
Find an equation of the line. Write the equation using function notation.
Through ; parallel to ( − 2, − 6) 5x + 2y = 7
f(x) =
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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Use the graph of the function shown to find all positive values of x such that .g(x) = 8
x = (Use a comma to separate answers as needed.)
10 8 6 4 2 2 4 6 8 10
10
8
6
4
2
2
4
6
8
10
x
y
g(x)
The function can be used to predict diamond production. For this function, x is the number of years after 2000, and f(x) is the value (in billions of dollars) of the year's diamond production. Use this function to predict diamond production in
f(x) = 0.42x + 13.4
2010.
The diamond production in is predicted to be $ billion.2010 (Type an integer or a decimal.)
Graph the function.
f(x) =2x, for x < 0
x + 1, for x ≥ 0
Choose the correct graph below.
A.
10 10
10
10
x
y
B.
10 10
10
10
x
y
C.
10 10
10
10
x
y
D.
10 10
10
10
x
y
Sketch the graph of the function.
f(x) = + 1x
Choose the correct graph below.
A.
10 10
10
10
x
y
B.
10 10
10
10
x
y
C.
10 10
10
10
x
y
D.
10 10
10
10
x
y
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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35.
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Sketch the graph of the function.
y = ( )x − 3 2
Choose the correct graph below.
A.
16 162
30
x
y
B.
16 16
16
16
x
y
C.
16 16
16
16
x
y
D.
16 162
30
x
y
Find the graph of the function.
g(x) = − + 3x − 1
Choose the correct graph below.
A.
10 5 5 10
105
510
x
y
B.
10 5 5 10
105
510
x
y
C.
10 5 5 10
105
510
x
y
D.
10 5 5 10
105
510
x
y
Graph the equation.
y = 3
Choose the correct graph below.
A.
10 10
10
10
x
y
B.
10 10
10
10
x
y
C.
10 10
10
10
x
y
D.
10 10
10
10
x
y
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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Graph the following equation.
x = 5
Choose the correct graph below.
A.
10 10
10
10
x
y
B.
10 10
10
10
x
y
C.
10 10
10
10
x
y
D.
10 10
10
10
x
y
Write the domain and range of the function.
h( ) = − |x + 5| + 1x
The domain is . (Type your answer in interval notation.)
The range is . (Type your answer in interval notation.)
Without graphing, find the domain of the function.
f( ) = 3 + 1x x − 16
The domain is . (Type your answer in interval notation.)
If y varies directly as x, find the constant of variation and the direct variation equation for the situation.
y when x= 10 = 4
The constant of variation k is . (Type an integer or a simplified fraction.)
The direct variation equation is y = . (Use integers or fractions for any numbers in the expression.)
If y varies inversely as x, find the constant of variation k and the inverse variation equation for the situation.
y when x= 6 = 5
Find the constant of variation k.
k (Simplify your answer.)=
Write the inverse variation equation.
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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1.
A. (Simplify your answer.)x + 3
x2 − 5x − 24=
1x − 8
2. x2
77
3. x + 6
x
4. 2w5
5. 2x2
5
6. 4
7. 1427
8. x27
9. 6x + 5y2(x + 3y)
10. 2
5(x − 5)
11. y + 65 + y
12. 5x + 11
13. 1
x − 3
14. x + 4
15. 2
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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16.
15x + 73x2
17. x − 72
(x + 8)(x − 8)
18. 3x + 15x + 2
19. x2 + 3x
(x − 5)(x − 3)
20. 11.5
21. 4 12
22. 19.5
23.
10 8 6 4 2 2 4 6 8 10
10
8
6
4
2
2
4
6
8
10
x
y
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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24.
10 8 6 4 2 2 4 6 8 10
10
8
6
4
2
2
4
6
8
10
x
y
25. 5x − 34
26. − 9x + 45
27. 3x − 7
28. − 4
29. − 5x + 5
30. − x − 1152
31. 6
32. 17.6
33. B.
10 10
10
10
x
y
5/18/2016 Final Exam Review Ch 7-8-Virginia Davis
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34. C.
10 10
10
10
x
y
35. D. 16 162
30
x
y
36. D.
10 5 5 10
105
510
x
y
37. C.
10 10
10
10
x
y
38. C.
10 10
10
10
x
y
39. ( − , )
( − ,1]
40. [16, )
41. 52
x52
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42. 30
y = 30x
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