Name ______________________
Period_________
Semester Exam Review
1.Write the equation of the line containing (-2,6) and (4, -3).
2. Give the slope of a line perpendicular to the line in #2.
3. (-2,3) (-4,2) (2,3) (1,5) (-2,5)
4. (1,5) (2,6) (3,7) (4,8)
Domain:________________
Domain:________________
Range:_________________
Range:_________________
Zeros:__________________
Zeros:__________________
Function: Y or N
5.
Function: Y or N
6.
Domain:________________
Domain:________________
Range:_________________
Range:_________________
Zeros:__________________
Zeros:__________________
Function: Y or N
Function: Y or N
Simplify the following expressions.
3
 5 y 3  6 y 4 



7.
 3 x 2 


9.
27x 5 y 2
9x 8 y
10.
 3xy 


 2
 2x 
11.
5a
5a3
12.
4 x  3  5x 2
8.
2
_____13. Using f(x) = x2 – 5 and g(x) = x + 2 , Find f(g(2))=
_____14. Using f(x) = x2 – 5 and g(x) = x + 2 , Find g(f(x))=
_____15. Give the equation of the line containing (-1,5) and (3,7).
_____16. The slope of the line parallel to the graph of 2x - 5y = 10 is ______.
_____17. Using the function f(x) = 3x2 – 14x – 5 , the axis of symmetry equation is
_____18. Start with f(x). Which notation would reflect f(x) across the y-axis?
_____19. Start with f(x). How would f(x–4)+3 change the graph?
_____20. Start with f(x). How would 2f(x) change the graph?
21. How many real zeros does
f  x   x4  6x3  3x2  14x  2 have?_____________________
22. Find the roots of f ( x)  x3  5 x 2  3x  11 _________________________
23. 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  5x 2  28x  13 _________________
c)
b) f ( x)  x3  5x 2  4 x  13_____________________
f ( x)  2 x2  3x  4 ___________________
24. Describe the transformations compared to the parent graph.
a)
y  x  2  7 ________________________________________________
b)
y  x  5  8 ___________________________________________________
c)
y   3 x  18   2 ______________________________________________
d)
y   4 x  12   6 ______________________________________________
2
3
25. State the equation of the function generated by translating the parent graph
y  x 3 four units to the right and 8 units up.
_____________________________________________
26. Find the inverses of the following functions
a)
f ( x)  ( x  9)3 __________________
b) f ( x)  x 2  5 ____________________
27. 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)
28. For
 x 2  5, x  3 , what is the value of f (3) ?
f ( x)  
 x  7, x  3
______________
29. Find the slope and y-intercept of the equation of the line passing through (-10,8) and (7, 3).
30. Write the slope intercept form of the equation of the line parallel to y =

3
x – 6 & passing through (0, 4).
4
31. Write the slope intercept form of the equation of the line perpendicular to y = -3x – 6 and passing through the point (7, -8).
Find the inverse of the function. Is the inverse a function? Write yes or no.
32. y = 6 – 2x
33. 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.
34. y =
x 3  3x 2  4
35.
______________________
y  4  x  x2
_____________________
36. Find the x- and y-intercepts of
y  x 2  6 x  11.__________________________
37. 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 ______________________________________
38. 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
________________
39. What is the relative maximum point of the graph of y = -x 2 - x +3?_________________
40. What point is a relative minimum of the graph of f(x) = x3 - 4x 2 -5x +14?_______________
41. Write the polynomial equation of least degree for the set of roots
 4i, -5 ________________
42. Write the polynomial equation of least degree for the set of roots
 6, -5, 3_______________
43. Solve the equation by using the quadratic formula 3x2 - 12x + 4 = 0.____________________
44. Find the remainder for each division using synthetic division. Is the binomial a factor of the polynomial?
x4  x2  2
x3
Simplify.
45. (j5)-2

9
46. 36 y
(j4)-5
3y2
Evaluate using upside-down division.
47.
4
243x7 y 3
48.
75s8
49. Simplify i33.
50. Simplify (5 – 3i) + (-10 – 8i)
51. Simplify (3 - i)(4 + 2i)
52. Simplify 1 + 3i
2 + 5i
53. Complete the following Trig Identities.
a) sin

=______________
d) csc

= _____________
b) cos

=_______________
e) sec

= ______________
c) tan

= ______________
f) cot

= _______________
54. For right triangle ABC, if A = 22o, B = 90o, c = 10, find the measure of side b.
55. 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?
56. Given: f(x) = 3x – 2
g(x) = x2 + 5
a. f(-3) = ________________________
b. f(g(4)) = ________________________
c. (f+g)(x) = ________________________
d. (f(g(x)) = ________________________
57. 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.
58. sin 

13
17
Quadrant II
59. tan

5
7
Quadrant III
III. Find the values for
State
60.

1
2
1
2
__________
cos   

65.
__________
sin  

63.
3
2
66. cos   
0 and 2 .
61.
__________
64. sin  

1
2
__________
62. cos  

for which each equation is true. Draw the angles.
in radians between
sin   


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.
67.
sin
68. cos
69.
5

3
13

4
 5
tan  
 6



70.
2

3
sin
9

4
71. cos
3

2
72.
tan
73.
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.
74. 84
77.

75. -350
16
9
78. 114


76.
10
13
79.
 14
11
If each angle has the given measure and is in standard position, determine the quadrant in
terminal side lies.
80. a)
7
12
b)
346
c)

25
13
D)
 545
Find the reference angle for each angle with the given measure.
81. a)
300
b)
 7
3
c)
645
d)
15
7
which its
Simplify the following rational expressions.
81.
5 x  15
x 2  3x
a).
38k 2 m 2 n
24k 4 mn5
16 x 2 y 5 z
82.
8x 3 y 2 z 2
a).
6 x  18 x 3

83.
4x2 2x  6
x3
x2
 2
a).
4 x  4x  3
84.
85.
86.
x 2  2 x 3x  6

6
x
5 2

6x 3
3
2y
 2
y  3 y  7 y  12
a).
a).
a).
x 2  6x  8
x 2  2 x  24
m 2  2m  8
2m  8
 2
8m  24
m  7m  12
2
7

5 x  20 x  4
5
7

4 x 12 x
b).
b.
7 x  14
x 2  2x
9x  9
x  8x  7
2
5 x 2  6x  7

b).
x  1 3x  21
b).
x3
x2
 2
10 x  20 x  4 x  3
b).
7
4

x  2 3x  6
b).
2
3

x 5 x 7