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Name:______________________________________
Chapter 8 Test Review
Write a function that models each variation.
1. x = 1 when y = 5. y varies inversely as x.
2. x = 3 and y = 12 when z = 2. z varies directly with y and inversely with x.
For each rational function, identify any holes and asymptotes (horizontal or vertical) of its graph.
Also give the domain and range of each function.
3. y 
x
x 3
4.
x 2  5x  6
x 2  3x  2
Holes:
Holes:
VA:
VA:
HA:
HA:
Domain:
Domain:
Range:
Range:
5. y 
x3
x

2

 x  3
6.
y
Holes:
Holes:
VA:
VA:
HA:
HA:
Domain:
Domain:
Range:
Range:
7. y =
x 2 – 36
x+1
8. y 
1
3
x4
 x – 2  x + 4 
 x + 2  x – 3
Holes:
Holes:
VA:
VA:
HA:
HA:
Domain:
Domain:
Range:
Range:
Name:______________________________________
Sketch the graph of each rational function.
x
9.
10.
y
x  x  2
y
1
3
x4
VA:
VA:
Holes:
Holes:
HA:
HA:
X intercepts:
X intercepts:
Domain:
Domain:
Range:
Range:
Simplify each rational expression.
3 x 2  12
11.
x2  x  6
13.
2
x

x5 x5
12.
2 x2  x
x

4 x2  4 x  1 8x  4
14.
3x
1
 2
x 4 x
2
Name:______________________________________
15.
17.
19.
16.
y
y
–
y– 1 y – 2
x y
2x – y
18.
x+y
2x + y
x 4
x  2
 2
x  2x  8
x  16
2
2
3
3
1

4
3
1 
20.
x 2 + 2x – 15
x2 – 4

x– 3
2
4 x 10y 4

5 y 24 x3
1
x
1
5 
y
1 
21.
Name:______________________________________
Solve each equation. Check each solution.
22.
24.
x x
  10
3 2
9
3
3
+
=
28 x + 2 4
23.
y  3 y 1

5
7
25. x +
x2 – 5
x2 + x + 2
=
x 2 –1
x+1
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