Name_____________________________________________Date_______________Block__
Precalculus S Review for Final – Chapters 1 and 2
Directions: Find the answer that best completes the statement or answers the question.
1. Describe the set of numbers using interval notation.
x > 8 or x ≤ 2
2. Describe the set of numbers using set-builder notation.
all multiples of 10
3. Find f(–4) for f(x) = 3x2 + 7x – 8.
4. Find f(t – 3) for f(x) = 4x2 – 8x + 4.
Use the graph to determine the domain and range of the relation, and whether the relation is a function.
5.
6. Determine the domain of the function
Page 1
7. Which of the following graphs is a function?
a.
b.
c.
d.
8. Use the graph below to identify the y-intercept and zeros.
9. Use the graph below to find the domain and range.
Page 2
10. Determine whether the graph of
is odd or even.
11. One of the following functions is neither odd nor even. Which one?
a. x7 + 3x5 + 6x
b. 6x6 – |x6| + 3
c. x6 + 3x + 3 + |x – 3|
d. x5 + 3x
12. The graph below is a portion of a complete graph. Complete graph assuming it is an even function?
13. Determine between which consecutive integers the real zeros of
[–10, 10]. If the zero occurs at an integer, write the integer.
are located on the interval
14. Describe the end behavior of the graph.
Page 3
Without graphing, describe the end behavior of the graph of the function.
15.
16.
17. Describe the end behavior of the graph.
For 18-20 Estimate and classify the critical points for the graph of each function.
18.
19.
Page 4
20.
21. Graph the function defined by
a.
b.
c.
d.
22. Graph the function defined by
a.
b.
c.
d.
Page 5
23. Graph y = |x + 1|
24. Find (f g)(x) and (f g)(x) for f(x) = 8x2 + 52x + 72 and g(x) = 4x + 8.
25. Find (f + g)(x) and (f g)(x) for f(x) = 6x2 + 5 and g(x) = 7 – 5x.
26. State the domain of f g. Then find f g, including any additional restrictions necessary on the domain of the
composition.
f(x) =
g(x) =
27. State the domain of f g. Then find f g, including any additional restrictions necessary on the domain of the
composition.
f(x) =
g(x) =
28. Given f(x) = x2 + 7 and g(x) =
. Find (g ° f)(4).
Page 6
29. Given
find
Then state whether
is a function.
Determine whether f has an inverse function. If it does, find the inverse function and state any restrictions on its
domain.
30. f(x) =
31. Solve.
+ 1 = 11
32. Solve
.
33. State the number of possible real zeros and turning points of f(x) = x4 – 13x2 + 36. Then determine all of the real zeros
by factoring.
Page 7
34. Graph f(x) =
.
a.
b.
c.
d.
35. Graph f(x) =
.
36. Determine the zeros for and the end behavior of f(x) = –x(x + 1)(x + 3)4.
37. Factor x3 – 2x2 – 19x + 20 completely using long division if (x – 1) is a factor.
38. Use the remainder theorem to find which of the following is not a factor of x3 + 2x2 – 9x – 18.
Page 8
39. List all of the possible rational zeros of f(x) = 5x4 – 7x3 – 7x2 + 8x + 6.
40. Find the domain of and the equations of any vertical or horizontal asymptotes for g(x) =
41. Find the domain of and the equations of any vertical or horizontal asymptotes for g(x) =
42. Which is a graph of
.
.
with any vertical or horizontal asymptotes indicated by dashed lines?
a.
b.
c.
d.
Page 9
43. Graph f(x) =
a.
b.
c.
d.
44. Graph f(x) =
45. Which is a graph of
with any vertical or horizontal asymptotes indicated by dashed lines?
a.
b.
c.
d.
Page 10
46. Solve.
=
Solve each equation.
47.
48. Use a sign chart to solve (4x + 7)(x + 9) ≥ 0.
Solve each inequality. Round to the nearest hundredth.
49. 4x2 – 3x – 3 > 2x2
50.
Page 11
Answer Key
1. c
2. b
3. a
4. a
5. c
6. c
7. d
8. a
9. c
10. b
11. c
12. c
13. a
14. b
15. a
16. c
17. a
18. c
19. b
20. d
21. c
22. a
23. c
24. d
25. d
26. b
27. a
Page 12
28. c
29. a
30. b
31. a
32. c
33. b
34. c
35. b
36. a
37. c
38. d
39. b
40. c
41. a
42. c
43. a
44. d
45. a
46. a
47. b
48. b
49. d
50. b
Page 13