Name: ________________________ Class: ___________________ Date: __________
ID: A
On-Level First Semester Algebra II Exam Review
Graph the function and its parent function. Then
describe the transformation.
Write an equation of the parabola shown.
14.
1. g(x) = 4| x|
2. g(x) =
1
| x|
3
3. g(x) = 3| x|
4. g(x) = 2 (x + 2 ) − 2
2
5. g(x) = −3 (x + 2 ) − 3
2
6. g(x) = −3 (x − 2 ) − 3
2
Write a rule for g described by the
transformations of the graph of f. Then identify
the vertex.
15.
2
7. f (x ) = x ; vertical stretch by a factor of 2 and a
reflection in the x-axis, followed by a translation
1 unit right.
8. f (x ) = x 2 ; vertical shrink by a factor of
1
and a
2
reflection in the x-axis, followed by a translation
4 units up.
2
9. f (x ) = x ; vertical shrink by a factor of
1
and a
3
reflection in the y-axis, followed by a translation
4 units left.
4
10. f (x ) = x − x − 2, g (x ) = 2f (x )
Find the minimum or maximum value of the
function. Describe the domain and range of the
function, and where the function is increasing and
decreasing.
11. h (x ) = 2x 2 − 8x + 2
12. h (x ) = −4x 2 − 8x + 1
13. h (x ) = −x 2 + 6x − 4
1
Name: ________________________
ID: A
28. x 2 + 13x < –36
16.
Describe the end behavior of the graph of the
function. Hint: Rewrite in standard form
29. h (x ) = −14x − 11 − 14x 4 + 10x 2 − 6x 7
30. g (x ) = −9 − 12x 3 − 2x 4 − 3x 2 − x
31. g (x ) = 5 − 3x 3 − 14x 2 − 9x 7 − 8x
Find the difference.
32.
(x 4 + 4x 3 − 5x 2 + 4x − 4) − (3x 4 + 7x 3 − 6x 2 + 6x + 9)
Solve the equation.
33.
17. x + 49 = 0
(−8x 4 − 6x 3 + 7x 2 + 5x − 3) − (−x 4 + 9x 3 + 9x 2 − 9x + 2)
18. x 2 − 16 = 0
Divide using synthetic division.
2
19. 3x =
1 2
x + 10
5
20. 4x =
1 2
x +9
3
21. 2x =
1 2
x +3
4
34. (2x 4 + 6x 3 − 3x + 8) ÷ (x + 1)
35. (2x 4 + 4x 3 + 6x + 12) ÷ (x + 1)
Use synthetic division to evaluate the function for
the indicated value of x.
22. x 2 + 4x + 4 = 25
2
36. f (x ) = 2x + 19x + 13 ; x = −9
23. x 2 − 8x + 16 = 3
2
37. f (x ) = 4x − 24x + 19 ; x = 5
Solve the system.
Factor the polynomial completely.
2
24. y = (x − 2) − 4
38. a 3 − 49a
y = −4
39. t 3 − 9t
25. Graph y > (x − 3 ) − 3.
40. 20s 7 + 73s 6 + 63s 5
26. Graph y ≤ − (x − 3 ) + 2.
41. 8n 8 + 10n 7 + 3n 6
2
2
42. 6m5 + 48m2
Solve the inequality. Round decimal answers to
the nearest hundredth.
43. 2m11 − 128m8
44. m3 − 10m2 − 36m + 360
27. x 2 + 12x < –32
2
Name: ________________________
ID: A
45. r 3 + 9r 2 − 4r − 36
Find all real solutions of the equation.
46. x 3 − 6x 2 + 3x + 10 = 0
47. x 3 + 10x 2 + 31x + 30 = 0
48. x 3 + 16x 2 + 71x + 56 = 0
49. x 3 − 12x 2 + 27x + 40 = 0
50. f (x ) = x 6 , g (x ) = −3x 6
Perform the operation. Write the answer in
standard form.
51. (−1 + 4i) (9 − 4i)
a. 7 + 45i
b. 7 + 40i
c. −25 + 45i
d. −25 + 40i
52. (4 − 6i) (−7 + 9i)
a. −82 + 78i
b. 26 − 14i
c. −82 − 14i
d. 26 + 78i
53. (1 + 7i) (−8 + 9i)
a. 55 − 8i
b. −71 − 47i
c. 55 − 47i
d. −71 − 8i
3
ID: A
On-Level First Semester Algebra II Exam Review
Answer Section
1.
The graph of g is a vertical stretch of the parent absolute value function.
2.
The graph of g is a vertical shrink of the parent absolute value function.
3.
The graph of g is a vertical stretch of the parent absolute value function.
1
ID: A
4.
The graph of g is a translation 2 units
left, a vertical stretch, and a translation 2 units down of the parent quadratic function.
5.
The graph of g is a translation 2 units
left, a vertical stretch, a reflection in the x -axis, and a translation 3 units down of the parent quadratic function.
6.
The graph of g is a translation 2 units
right, a vertical stretch, a reflection in the x -axis, and a translation 3 units down of the parent quadratic function.
2
7. g (x ) = −2 (x − 1 ) ; ÊÁË 1,0 ˆ˜¯
1
8. g (x ) = − x 2 + 4; ÁÊË 0,4 ˜ˆ¯
2
2
ID: A
9. g (x ) =
1
2
(x + 4 ) ; ÊÁË −4,0 ˆ˜¯
3
10. g (x ) = 2x 4 − 2x − 4
The graph of g is a vertical stretch by a factor of 2 of the graph of f.
11. The minimum value is –6. The domain is all real numbers and the range is y ≥ −6 . The function is decreasing to the
left of x = 2 and increasing to the right of x = 2 .
12. The maximum value is 5. The domain is all real numbers and the range is y ≤ 5 . The function is increasing to the
left of x = −1 and decreasing to the right of x = −1 .
13. The maximum value is 5. The domain is all real numbers and the range is y ≤ 5 . The function is increasing to the
left of x = 3 and decreasing to the right of x = 3 .
1
14. y = x 2 + 2
4
1 2
15. y =
x +3
12
1
16. y = − x 2 − 2
8
17. no real solution
18. x = 4 and x = −4
19. x = 5 and x = 10
20. x = 3 and x = 9
21. x = 2 and x = 6
22. x = −7 and x = 3
23.
24.
x = 4±
ÊÁ 2, −4 ˆ˜
Ë
¯
3
3
ID: A
25.
26.
27.
28.
29.
30.
31.
−8 < x < −4
−9 < x < −4
h (x ) → ∞ as x → −∞ and h (x ) → −∞ as x → ∞
g (x ) → −∞ as x → −∞ and g (x ) → −∞ as x → ∞
g (x ) → ∞ as x → −∞ and g (x ) → −∞ as x → ∞
32. −2x 4 − 3x 3 + x 2 − 2x − 13
33. −7x 4 − 15x 3 − 2x 2 + 14x − 5
7
34. 2x 3 + 4x 2 − 4x + 1 +
x+1
4
35. 2x 3 + 2x 2 − 2x + 8 +
x+1
36. f (−9) = 4
37. f (5) = −1
38. a (a + 7) (a − 7)
39. t (t + 3) (t − 3)
40. s 5 (5s + 7) (4s + 9)
41. n 6 (2n + 1) (4n + 3)
4
ID: A
42. 6m2 (m + 2)(m2 − 2m + 4)
43.
44.
45.
46.
47.
48.
49.
50.
2m8 (m − 4)(m2 + 4m + 16)
(m + 6)(m − 6) (m − 10)
(r + 2)(r − 2) (r + 9)
x = −1, x = 2, and x = 5
x = −5, x = −3, and x = −2
x = −8, x = −7, and x = −1
x = −1, x = 5, and x = 8
The graph of g is a vertical stretch by a factor of 3 and a reflection in the x-axis of the graph of f.
51. B
52. D
53. B
5