Math Analysis 2013-2013 Semester 1
Midterm Review Use extra paper to work the problems if needed. Do not use calculators except where indicated
Chapter 10: Matrices
A = B = C =
Using the above matrices, find the following products if possible 1. AB =
2. BA =
3. AC =
4. CA =
5. BC =
6. CB =
Find the inverse of each Matrix
7. A-1 =
8. B-1 =
9. C-1 =
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Solve each system using inverse matrices, row operations and Cramer’s Rule (do all 3 for each)
10. 2x -5y = 2 3x – 7y = 1
11. 2x + 6z = -9 3x -2y + 11z = -16 3x – y +7z = -11
Chapter 2 & 3: Functions and Transformations:
Use the functions f(x) = 4x -2 and g(x) = x2 + 5, find
12. f(6)
13. g(-13)
14. f(x) + g(x)
15. f(x)g(x)
16. f(g(x))
17. g(f(x)
18. (f-g)(-2)
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Identify the domain and range for each function in interval notation
19. f(x) =
20. g(x) =
21. Find the equation of the vertical asymptote(s) for the function: 2
2
7 12( )
2 15x xf xx x
22. Find the equation of the horizontal or slant asymptote for the function: 23 8 3
( )3
x xf xx
23. Is the function f(x) = 3x4-2 odd, even or neither?
24. How does the graph of f(x) = 3(x-4)2 + 6 differ from g(x) = -2(x+4)2 -3?
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−9 −8 −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 8 9 10
10
−9
−8
−7
−6
−5
−4
−3
−2
−1
1
2
3
4
5
6
7
8
9
x
y
25. Given the polynomial equation, 2
( ) 5 3f x x x x
= + − , label the zeros and intercepts
a. Identify the degree: __________
b. Describe the end behavior As _________ As _________
c. Identify the zeros and their multiplicities:
_______ multiplicity of _____
_______ multiplicity of _____
_______ multiplicity of _____
d. Sketch the curve using the information from above.
, ( )x f x→∞ →
, ( )x f x→−∞ →
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26. Graph the following and give the domain and range
Domain _________________ Range __________________
27. Graph the following. Give the domain and range, all intercepts, any asymptotes and holes
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Domain _________________________ Range ____________________ Intercepts ____________________________
Holes __________________________ Asymptotes ______________________________
28. Graph the following. Give the domain and range, all intercepts, any asymptotes and holes
Domain _________________________ Range ____________________
Intercepts ____________________________
Holes __________________________
Asymptotes ______________________________
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29. Below is a graph of f(x), answer the following questions
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Chapter 4: Logarithms and exponential functions
Find the domain and range of each log function
30. f(x) = log8(7-2x) + 5
31. g(x) = log12(x2 – 7x – 18)
32. h(x) =
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46. A child’s grandparents wish to purchase a bond that matures in 18 years to be used for her college education. The bond pays 4% interest compounded semiannually. How much should they pay so that the bond will be worth $85,000 at maturity?
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47. If x is the atmospheric pressure (measured in millimeters of mercury), then the formula for the altitude h(x) (measured in meters above sea level) is
48. ( ) (30 8000) log oPh x Tx
= +
where T is the temperature (in degrees Celsius) and Po is the atmospheric pressure at sea level, which is approximately 760 millimeters of mercury.
At what height is a Piper Cub whose instruments record an outside temperature of 0o C and a barometric pressure of 300 millimeters of mercury?
How high is a mountain if instruments place on its peak record a temperature of 5o C and a barometric pressure of 500 millimeters of mercury?
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Chapters 5, 6, & 7: Trigonometry
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Chapter 9: Conics
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Chapter 8: Polar Coordinates and Vectors
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Use the vectors v = -2i + j and w = 4i – 3j to find:
101. v – w
102. –v + 2w
103.
Determine whether v and w are parallel, orthogonal, or neither
102. 2 ; 2= − − = +v i j w i j
103. 3 4 ; 6 8= − = − +v i j w i j
104. 4 2 ; 2 4= − + = +v i j w i j
The vector v is represented by the directed line segment PQ
. Write v in the form ai + bj and find v .
105. P = (-3, 1); Q = (4, -2)
106. P = (3, -4); Q = (-2, 0)
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