Download Algebra 2 Quiz Review 9

Algebra 2 CP
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Assignment: H11
Chapter 8 Test Review
Graph each rational function. Determine (a) the equations of any vertical asymptotes, (b)the
equations of any horizontal asymptotes (c) x-intercepts, (d) y-intercepts (e) Domain, (f) Range.
Note: please state if none exist!
2
3
2
1. f  x  
2. f x  
x 1
x2
Vertical Asymptote:
Vertical Asymptote:
Horizontal Asymptote:
Horizontal Asymptote:
Domain:
Domain:
Range:
Range:
x-Intercept:
x-Intercept:
y-intercept:
y-intercept:
3.
f x  
3x 2
x2  1
4.
f x  
x2
1 x
Vertical Asymptote:
Vertical Asymptote:
Horizontal Asymptote:
Horizontal Asymptote:
Domain:
Domain:
Range:
Range:
x-Intercept:
x-Intercept:
y-intercept:
y-intercept:
5.
f x  
5
x  4x  3
2
6.
f x  
12
4
x4
Vertical Asymptote:
Vertical Asymptote:
Horizontal Asymptote:
Horizontal Asymptote:
Domain:
Domain:
Range:
Range:
x-Intercept:
x-Intercept:
y-intercept:
y-intercept:
7.
f ( x) 
x
x 1
2
Vertical Asymptote:
Horizontal Asymptote:
Domain:
Range:
x-Intercept:
y-intercept:
Simplify each expression.
3
24b 3 10bc 
8.

5c 2
8b 5c
11.
16 y 2  40 y  25
4y  5
 2
2
3 y  10 y  8
y  8 y  16
9.
3a 2
3a
 2
a2 a 4
12.
10.
x 2  19 x  84
2x  2
 2
4x  4
x  9 x  14
x
3
13.
x
1
2
14.
x 2  100
x2
15.
2
3 x  31x  10
2x
n4
16. n 2  6n  9
n  2n  8
3 n
2
32 x 4 y 8 xy2

3 xy2 21 y 4
x
x 1
x
1
2
2
2
17.
16
2

x  16 x  4
18.
5
7

6ab 8a
19.
2  5m 4 m  5

m9
9m
20.
1 3
7
 
5n 4 10n
21.
2m  3
5
 2
m  5m  6 m  9
22.
x2
x
 2
x  x  12 x  2 x  3
2
2
Solve each equation or inequality.
x  2 2x  4

23.
x
3
2
24. 5 
3 7

a a
25.
x
x
 1 
x 1
2
27. 2 
x2
x2

x3
x6
x2  4
x
2


29. 2
x 4
x2
x2
26.
4
1
1


p
3p
5
28.
4v
5v
2

 2
v 1
v2
v  3v  2
30.
x
2
x 2  20


2x  1 2x  1 4x2  1
ANSWERS
1.
VA: x = 1
HA: y = 0
D: x ≠ 1
R: y ≠ 0
x-int: None
y-int: (0, -2)
2.
VA: x = -2
HA: y = 2
D: x ≠ -2
R: y ≠ 2
x-int: (-1/2, 0)
y-int: (0, 1/2)
3.
VA: x = ±1
HA: y = 3
D: x ≠ ±1
R: y > 3 and y ≤ 0
x-int: (0, 0)
y-int: (0, 0)
4.
VA: x = 1
HA: None
D: x ≠ 1
R: y ≥ 0 and y ≤ -4
x-int: (0, 0)
y-int: (0, 0)
5.
VA: x = 3,1
HA: y = 0
D: x ≠ 3, 1
R: y > 0 and y ≤ -5
x-int: None
y-int: (0, 5/3)
6.
VA: x = 4
HA: y = 4
D: x ≠ 4
R: y ≠ 4
x-int: (1, 0)
y-int: (0, 1)
7.
VA: x = ±1
HA: y = 0
D: x ≠ ±1
R: ARN
x-int: (0, 0)
y-int: (0, 0)
8. 6b
13.
9.
a(a-2)
26  x 
32  x 
20  21b
24ab
17.
2
x4
21.
2m 2  2m  1
m  3m  3m  2
24. a = 2
29. No Solution
18.
25. x = 2, -1
10.
28x2y
11.
14.
23x  2
2  x x  1
15.
19.
 9m  7
m9
22.
2 x  1x  2
x  4x  3x  1
20.
4 y  5 y  4
3y  2
2 x  10 
x3 x  1
x  12
2x  2
16.
1
n  2n  3
36  5n 
20n
23. -2, 3
2
26. p = 65
27. x = 14
3
3
30. x = 6, -3
12.
28. v = -2, -1