Download Semester Exam Review

Name ______________________
Period_________
Semester Exam Review
1. How many real zeros does
f  x   x  6x3  3x2 14x  2 have?_____________________
4
2. Find the roots of f ( x)  x3  5 x 2  3x  11 _________________________
3. Find the values of x, if any, for which the following functions have a relative maximum or a relative minimum.
a) f ( x)  4 x3  5 x 2  28 x  13 _________________
c)
b) f ( x)  x3  5x 2  4 x  13 _____________________
f ( x)  2 x2  3x  4 ___________________
4. Describe the transformations compared to the parent graph.
a)
y  x  2  7 ________________________________________________
b)
y  x  5  8 ___________________________________________________
c)
y   3x  18  2 ______________________________________________
d)
y   4 x  12   6 ______________________________________________
e)
y  x 2  8 x  11 ________________________________________________
2
3
5. State the equation of the function generated by translating the parent graph
_____________________________________________
6. Find the inverses of the following functions
a)
f ( x)  ( x  9)3 __________________
b) f ( x)  x 2  5 ____________________
y  x3 four units to the right and 8 units up.
7. What is the minimum possible degree of the polynomial of each function graphed? What is the function that describes the
graph?
a)
b)
c)
d)
8. For
 x 2  5, x  3 , what is the value of f (3) ?
f ( x)  
 x  7, x  3
______________
9. Find the slope and y-intercept of the equation of the line passing through (-10,8) and (7, 3).
10. Write the slope intercept form of the equation of the line parallel to y =

3
x – 6 & passing through (0, 4).
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11. Write the slope intercept form of the equation of the line perpendicular to y = -3x – 6 and passing through the point (7, -8).
12. Given f(x) =
a) (f + g)(x)
2 and g(x) = x2- 3, find each function.
x4
b) (f – g)(x)
c)  f  g 
13. Given: f(x) =
1
x+5
3
g(x) = x – 3
a)
Find [f  g](x)
b) Find [g  f ](x)
________________________
________________________
Find the inverse of the function. Is the inverse a function? Write yes or no.
14. y = 6 – 2x
15. Given f(x) = 8- x2, find f (-2). _______________________
Find the critical points of each function. Then determine whether each point represents a maximum, minimum, or a point of
inflection.
16. y =
x 3  3x 2  4
17.
______________________
y  4  x  x2
_____________________
18. Find the x- and y-intercepts of
y  x 2  6 x  11.__________________________
19. Describe the transformation(s) that have taken place from the parent graph of
2
f(x) = x .
a)
y=5x
2
____________________________________________
2
b)
y = -.75 x ___________________________________________
c)
y = 3(x – 5) __________________________________________
d) y =
2
1
2
(x + 4)
3
- 2 ______________________________________
20. Which graph has a maximum point?
a)
y= x 2 +6x + 11 ______________
b) y = x 2 + 8x + 21
c) y = -5x 2 - 30x + 51
______________
_______________
d) y = 8x 2 + 40x + 37 ________________
21. What is the relative maximum point of the graph of y = -x 2 - x +3?_________________
24. What point is a relative minimum of the graph of f(x) = x3 - 4x 2 -5x +14?_______________
25. Write the polynomial equation of least degree for the set of roots
 4i, -5 ________________
26. Write the polynomial equation of least degree for the set of roots
 6, -5, 3_______________
27. Solve the equation by using the quadratic formula 3x2 - 12x + 4 = 0.____________________
28. Find the remainder for each division using synthetic division. Is the binomial a factor of the polynomial?
x4  x2  2
x3
Simplify.
29. (j5)-2  (j4)-5
9
30. 36 y
3y2
Evaluate using upside-down division.
31.
4
243x7 y 3
32.
75s8
33. Simplify i33.
34. Simplify (5 – 3i) + (-10 – 8i)
35. Simplify (3 - i)(4 + 2i)
36. Simplify 1 + 3i
2 + 5i
37. Complete the following Trig Identities.
a) sin

=______________
d) csc

= _____________
b) cos

=_______________
e) sec

= ______________
c) tan

= ______________
f) cot

= _______________
38. For right triangle ABC, if A = 22o, B = 90o, c = 10, find the measure of side b.
39. For right triangle ABC, if A = 22o, B = 90o, c = 10, find the measure of side a.
40. In ABC, a = 5, b = 6, and c = 8. Find the measure of angle B.
41. In ABC, a = 5, b = 6, and c = 8. Find the measure of angle C.
42. In ABC, A = 63o, B = 19o, and a = 2.4. Find b to the nearest tenth.
43. In ABC, a = 5, b = 6, and c = 8. Find the measure of angle A.
44. In ABC, A = 112.0o, B = 21.8o, and c = 18. Find a to the nearest tenth.
45. Sean, who is 56 meters from the base of a tower, measures 17 o to the top of the tower. How high is the tower?
46. A train travels due west for 400 kilometers and then north for 350 kilometers. Find the train’s distance and direction from its
starting point.


II. Find the values of the six trigonometric functions of
. Assume that
is an angle in standard position whose terminal
side lies in the given quadrant. Draw and label the right triangle on the x-y plane.
47. sin 

13
17
Quadrant II
III. Find the values for
State
49.

1
2
__________

5
7
Quadrant III
for which each equation is true. Draw the angles.
in radians between
sin   


48. tan
0 and 2 .
50.
sin  

1
2
__________
51. cos  

52.
3
2
54.
__________
55. cos   
cos   

__________
53. sin  

1
2
1
2
__________
sin   0

__________
3
2

__________
III. Sketch the angle on the unit circle. Find and label the reference angle. Find each exact value. Do NOT use a
calculator.
56.
57. cos
58.
59.
5

3
sin
13

4
 5
tan  
 6
sin
60. cos
2

3
9

4



3

2
61.
tan
62.
sin 3 
Graph the following angles and label using both degree and radian measures. You will need a protractor for these
problems. You can use back of this paper or another sheet to draw the angles. Radians measures will have a Pi
symbol in it.
63. 84
66.

64. -350
16
9
67. 114


65.
10
13
68.
 14
11
If each angle has the given measure and is in standard position, determine the quadrant in
terminal side lies.
69. a)
7
12
b)
346
c)

25
13
D)
 545
Find the reference angle for each angle with the given measure.
70. a)
300
b)
 7
3
c)
645
d)
15
7
which its