Precalculus Quarterly Exam Study Guide #2. Multiple Choice: Identify the choice
that best completes the statement or answers the question. ____ 1. Determine ...
Name: _________________________________________
Date: _______________________
Precalculus Quarterly Exam Study Guide #2 Multiple Choice: Identify the choice that best completes the statement or answers the question. ____
____
1. Determine the domain of the function
a.
c.
b.
d.
2. Find
for
.
a. b. –125 ____
c. d.
3. Use the graph below to identify the y-intercept and zeros. y 70 60 50 40 30 20 10 –7
–6
–5
–4
–3
–2
–1 –10
1
2
3
4
5
6
7
x
–20 –30 –40 –50 –60 –70
a. y-intercept: 20 zeros: No zeros b. y-intercepts:2, –2 zero: 20
c. y-intercept: 20 zeros: 2, –2 d. y-intercept: –20 zeros: 2, –2
____
4. Use the graph below to find the domain and range. y 10 8 6 4 2 –10 –8
–6
–4
–2 –2
2
4
6
8
10
x
–4 –6 –8 –10
a. D: (–4, 1], (2, 8] R: (–9, 1.4] b. D: [–4, 1], [2, 8] R: [–9, 1.4]
____
5. For which interval(s) is the function increasing or decreasing?
a. b. c. d.
____
c. D: (–4, 1), (2, 8) R: (–9, 1.4) d. D: (–4, 8] R: (–9, 1.4]
increasing for increasing for increasing for increasing for
; decreasing for and
and
; decreasing for
; decreasing for and
and
; decreasing for
6. Which statement is true for the graph of a.
is a relative minimum;
is a relative maximum
b.
is a relative minimum;
is a relative maximum
c.
is a relative minimum;
is a relative maximum
d.
is a relative minimum;
is a relative maximum
____
7. Find (f + g)(x) and (f a. (f + g)(x) = (f g)(x) = b. (f + g)(x) = (f g)(x) =
____
8. Given
a.
8 7 b. 8
____
g)(x) for f(x) =
+8 8
and
and g(x) = c. (f + g)(x) = (f g)(x) = d. (f + g)(x) = (f g)(x) =
.
+8
Find
c.
6 7 d. –8
9. Solve: a. 7 b. –6
c. –3, 4 d. no real number solution
____ 10. Graph f(x) =
. y
a.
–20 –16 –12 –8
40
40
32
32
24
24
16
16
8
8
–4 –8
4
8
12
16
20
x
–20 –16 –12 –8
–4 –8
–16
–16
–24
–24
–32
–32
–40
–40 y
b.
–20 –16 –12 –8
y
c.
40
32
32
24
24
16
16
8
8
4
8
12
16
20
x
8
12
16
20
x
4
8
12
16
20
x
y
d.
40
–4 –8
4
–20 –16 –12 –8
–4 –8
–16
–16
–24
–24
–32
–32
–40
–40
____ 11. State the number of possible real zeros and turning points of f(x) = the real zeros by factoring. a. 3 real zeros and 2 turning points; 0, 3, and –1 b. 3 real zeros and 2 turning points; 0, –3, and 1
____ 12. Divide using long division: a. b. c. d.
. Then determine all of
c. 3 real zeros and 3 turning points; 0, –3, and 1 d. 3 real zeros and 3 turning points; 0, 3, and –1
÷
____ 13. Determine the equation whose roots are –3, –3, and 3. a. b.
c. d.
____ 14. List all possible rational zeros of
.
a. b. c. d.
____ 15. Use Descarte’s Rule of signs to describe the possible real zeros of the function: a. b. c. d. ____ 16. Write a polynomial function of least degree with real coefficients in standard form that has the given zeros: –6, –3, i a. b.
c. d.
____ 17. Find the vertical, horizontal, and oblique asymptotes, if any, for a. vertical: slant: b. vertical: slant: c. vertical: horizontal: y = 0 d. horizontal: y = 0 slant:
____ 18. Graph f(x) = y
a.
–20 –16 –12 –8
20
20
16
16
12
12
8
8
4
4
–4 –4
4
8
12
16
20
x
–3
–2
–8 –12
–16
–16
–20
–20
50
40
40
30
30
20
20
10
10
1
2
3
4
5
x
–50 –40 –30 –20 –10 –10
–20
–20
–30
–30
–40
–40
–50
–50
____ 19. Evaluate the expression:
____ 20. Solve
c. 2 d. 4 for x correct to four decimal places.
a. –0.4030 b. –0.4351
c. 0.7559 d. –0.7559
____ 21. Solve the equation: a. 14 b. 13
4
8
12
16
20
x
10
20
30
40
50
x
y
d.
50
–1 –10
a. 3 b. 5
–4 –4
–8
y
–4
–20 –16 –12 –8
–12
b.
–5
y
c.
c. –13 d. –3
____ 22. Solve the equation: a. b.
c. d.
____ 23. Solve the equation: a. –16.05 b. 16.05
c. 4.1 d. 45.03
____ 24. Solve the equation: a.
c.
b. infinite solutions
d.
____ 25. Solve a. b. 25
c. d. 32
____ 26. Find the values of the six trigonometric functions for angle , when
a.
5 , cos = 3 b. 4 sin = , cos = 5 c. 5 sin = , cos = 3 d. 4 sin = , cos = 5 sin =
5 , csc = 4 3 , csc = 5 3 , csc = 4 3 , csc = 5
3 4 3 4 , sec = , tan = , and cot = . 5 5 4 3 5 5 4 3 , sec = , tan = , and cot = . 4 3 3 4 3 4 4 5 , sec = , tan = , and cot = . 5 5 3 4 5 5 4 4 , sec = , tan = , and cot = . 3 4 3 3
and
.
____ 27. If
and
find . Round to the nearest tenth.
a. b. ____ 28.
c. d.
If
and
a. b.
a. b.
°
´ ° °
____ 30. Change
b.
. Round to the nearest tenth.
c. d.
____ 29. Write
a.
, find
35 54 35 18
´´ as a decimal to the nearest thousandth. c. d.
to radian measure in terms of . c.
35 36 d. 35 72
° °
____ 31. Write
in degrees
a. b.
c. d.
____ 32. Find the exact value of
.
a. 1
c.
b.
d. 0
____ 33. Find the exact value of sin
.
a.
c. undefined
b.
d.
Short Answer 34. State the domain and range of
, and determine whether the relation is a
function. 35. Use the graph below to identify the domain and range. y 10 8 6 4 2 –10 –8
–6
–4
–2 –2
2
4
6
8
10
x
–4 –6 –8 –10
36. Is the following function an even function, an odd function, or neither?
37. Describe how to determine the end behavior of the graph without graphing: 38. Are f(x) =
and g(x) =
39. Find
inverse functions?
by using synthetic division.
40. Determine all possible rational zeros of g(x) = zeros.
. Then determine which, if any, are
41. Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of f and g on the same set of axes: f(x) = 2x; g(x) =
42. Expand the expression:
43. Condense the expression: Solve each equation. 44. 45. 46. 47.
You will also want to look at the problems that we have completed on verifying trig identities and graphing sine and cosine functions. These will most likely appear on your quarterly exam as short answer problems
