AAT(H)
Semester Final Review
Name___________
FINAL REVIEW – Answers should be exact, for inequalities use interval notation to describe the
solution.
Solve
Given the function f  x  
1.
2.
5  7x
, state the domain in interval notation.
3x  9
Find the domain of the rational function.
f x  
3x  2
5x  3 x  2
3. Rewrite the quadratic equation in standard form by completing the square.
y  x 2  2x  7
y  x 2  12x  3
y  x 2  5x
4. Find the vertex of the parabola associated with the quadratic function and identify the
direction it opens.
y  (x  8)2  34
5.
y  (x  3)2  12
y  15(x  15)2  11
Solve by factoring. 6x 2  21x  12
6. Solve using the square root method.
(3x – 2)2 = 36
7. What number should be added to complete the square of the expression?
3
x2  x
7
8.
Simplify
15a 8b 3c
. Assume no variable equals 0.
12a 2b 7c 8

 
9. Simplify 8a 3  12a 2  2a  2a 3  3a 2  7

Simplify 3x  2  .
2
10.
75  18  48  300 .
11. Simplify
Divide and express the answers in the form of q(x) and r(x)
12. 7x 5  3x 4  2x 3  6x 2  5x  2  x 2  3x  4

 

13. Divide 18x 4  24x 3  12x 2  11x  3 by 3x + 1.


14. Evaluate 6x 4  52x 3  66x 2  20x  56   x  7 
15. State if the following is a polynomial and if so, state the degree
33
a . f (x )  24  15x 29
b . f (x )  14x 32  44x 23  5x 7  67 c . f (x )  23(x  2)26 (x  76)14 (x  5)
x
16. Find all the real zeros (and state their multiplicity) of the polynomial function. Identify the
behavior at each zero and the end behavior.
f (x )  x (x  6)3 (x 4  3)
f (x )  x 4  64
f (x )  x 4  784
17. Find f  4  for f  x   x 3  4x 2  5x  6
18. Find f  1  for f  x   2x 5  x 3  5x  27
19. f (3) for f (x )  x 7  4x 6  5x 5  2x  6
20. Solve x 3  3x 2  4x  12  0
21. Given that -2 is a zero of f (x )  x 3  3x 2  4x  12 , find the other real zeros
22. Determine whether -4 is a zero of the polynomial. If so, find the other real zeros
f (x )  x 3  3x 2  3x  4
23. Given the function f(x) =12x – 15, evaluate f(x -1).
24. Given the function f(x) = x2 – 3x + 5, evaluate f(x) – f(-3).
25. Given the functions f  x   3x  1 g  x   2x 2  4 ,
Find (f  g )( x )
(f  g )( x )
f (x)
g( x )
(f  g )( x )
26. Given the functions f  x   2x  1
g x   x 2  1
Find  f g  (-2),  g f  (4) ,  g f  ( x ) and f 1  x 
27. Given the functions f  x   x  1
g x   x 3  8
Find f g (3) and g f (8)
28. The graph of y = f(x) transformed into y = -f(-x)+2. Describe the transformation (WITHOUT
YOUR CALCULATOR)
29-32 Perform the indicated operation. Answers should be simplified
29.
64a 6 b9
 2ab 
3
6n  2
n3
30.
6n 2  16n  6
n5
4r 5 n 5 21t 2

3t 4 16r 3 n
x 2  10 x  25 x 2  1x  30

2x  2
x 1
m 2  8m  16 m3  8m

m 2  6m  8 m 2  8
31.
32.
2 3
4
 2
x x
2x
x 1
x

2x  1 3 x  2
1
5

x 1 x  2
1
3
2

 2
x  2 x  4 x  2x  8
33-42 solve for x, write answers using interval notation where appropriate
33.
2x
3x  10
 2
1
x 2 x  4
34.
36.
5x  1  2
37.
39.
x  4  7  15
40. x 2  25  10x
42. x 2  3x  10  0
solve by graphing
x 5
0
x 3
10x  51  x  4
35.
38.
x 7
0
x  15
x 5 2  3
41. x 2  7x  8
43. Given 3i is a zero of p  x   x 4  2x 3  14x 2  18x  45
Find all other zeros.
.
AAT(H) FINAL EXAMINATION REVIEW
NON CALCULATOR PORTION
Graph each quadratic, identify the vertex, state the domain and range.
 
2
1. f x  2x  12x  9
-10
-8
-6
-4
2
2. f  x   4  x  2  9
10
10
8
8
6
6
4
4
2
2
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8
10
Graph the functions described below
3. f  x   x  x  4  (x  5)3
2
-10
-8
-6
-4
4. f  x   x 4  x 3  12x 2  4x  16 ,
10
10
8
8
6
6
4
4
2
2
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
-1 and -4 are zeros
6
8
10
5. Given that -2 is a zero of the polynomial p  x   6x 3  13x 2  4 , determine all other zeros
6. Use the graph below to fill in the table to the right.
Minimum degree of poly_______
Behavior as x   _________
Behavior as x   _________
Sign of leading coefficient________
# of real zeros_________
Graph each equation
# of relative minimums_________
# of relative maximums________
8. f ( x)  2 3  x
7. f ( x)  2 x 1  6
10
10
8
8
6
6
4
4
2
2
-10
-8
-6
-4
-2
2
4
6
8
-10
10
-8
-6
-4
-2
2
4
6
8
10
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
10. f ( x)   x  3
9. f(x)  x3  2
10
10
8
8
6
6
4
4
2
2
-10
-10
-8
-6
-4
-2
2
4
6
8
-8
-6
-4
-2
10
2
4
6
8
10
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
x 2 , x  3



12. f  x    x  3 ,3  x  5


x  4, x  5

4, x  3



11. f  x   2x  1,  3  x  5 
x , x  5



-10
-8
D:
-6
-4
10
10
8
8
6
6
4
4
2
2
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
R:
D:
-10
4
R:
6
8
10
13. f  x  
x 3
x x 6
14. f  x   2 x  3  4
2
10
10
8
8
6
6
4
4
2
2
-10
-10
-8
-6
-4
-2
2
4
6
8
-8
-6
-4
-2
10
2
4
6
8
10
8
10
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
D:
R:
D:
15. f  x     x  1   5
16. f  x   2 x  2  3
3
-10
-8
D:
-6
-4
R:
10
10
8
8
6
6
4
4
2
2
-2
2
4
6
8
10
-10
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
R:
D:
4
R:
6