Alg2Trig
Name ____________________________
CHAPTER 8 EXTRA CREDIT
Show all work for full/partial credit. This packet is due April 12th (No Exceptions) 4pm.
Half of the points from this packet will go towards replacing points from the Chapter 7
test. You can not go over 100 points on the test.
Matching: Mark the letter of the asymptote(s) for each graph in the space provided. Some letters may be used
more than once, some not at all. Some questions may have more than one answer.
x 2
__________ 1. y 
x 2
__________ 2. f (x ) 
__________ 3. y 
__________ 4. y 
3x 2  3 x  1
x 2 1
A. x  2
G. y  1
B. x  1
H. y  1
3
3
x 2
C. x  2
I. y  3
D. x  1
J. y  3
3x  5
x2 4
E. x  3
K. y  x  2
F. No V.A.
L. y  x  4
__________ 5. f ( x ) 
x
2
M. y  0
x 4
2
N. No H.A.
__________ 6. f (x ) 
x  3x  2
x 1
2
7. Simplify the rational expression.
n2  2n  24
n2  11n  28
2
8. Simplify the rational expression. x  4
6
6
x
x2  6 x  8
9. What types of discontinuity does the function g ( x) 
have?
x2  4
___________________
___________________
10. Solve:
2
3
7g  9

 2
g  5 g  5 g  25
_________________
11. The variable z varies jointly with x and y. If z = 16 when x = 4 and y = -2, find the value of x if z = 96 and y = 4.
___________________
12. What is the horizontal asymptote of the function f(x) =
13.
2x 3  2
x 2  16
Where is the hole in the graph of the function f ( x ) 
14. What is (are) the vertical asymptote(s) of the function?
f(x) =
15. Multiply:
?
x2  x  6
x 3
__________________
________________
_________________________
x2  9
x 2  3x  18
6y  9 10x  40

x 2  16 10y  15
__________________
16. Select all of the following functions that have the same vertical asymptote as the graph shown.
x 2  25
a. f(x) = 2
x  16
c. f(x) =
x2  4x  5
x 2  8 x  15
e. f(x) =
1
5
x5
17. Divide:
x 2  10x  21 x  7

x 7
x2  9
4
2

19. Simplify: x  9 x  3
1
1

x 3 x 3
y
2
3
b. f(x) =
x5
d. f(x) =
x 2  x  20
x 2  25
8
8x
–8
–8
18. Add:
4
1

x 2 x 2
2
20. Subtract:
x
3x  1

x 4 x2
2
6
8x2
4x
 2

21. Solve:
x 3 x 9 x 3
Solution(s)___________________
22. Graph the function and identify all information listed below.
2
f(x) =
4
x2
V.A.:_____________
H.A.:____________
x-int:_____________
y-int:____________
Hole______________
Domain:_________________________
Range:__________________________
23. Graph the function and identify all information listed below.
x 2  4x  5
f(x) = 2
x x 2
V.A.:____________
H.A.:_____________
x-int:____________
y-int:_____________
Hole____________
Domain:_________________________
Range:__________________________
24. Write an equation in H-K form for the function of the given graph.
6
4
2
-5
5
-2
-4
10