Algebra 2 - Chapter 9 Test
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Date:
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Suppose that x and y vary inversely. Write a function that models the inverse variation
and find y when x = 18.
1) x = 12 when y = 6.
Write the function that models the variation. Find z when x = 3 and y = 5.
2) z varies directly with x and inversely with y and when z = 30, x = 2 and y = 7.
The pair of values is from a direct variation. Find the missing value.
3) (8,28), (18,y)
Make a table of values. Then sketch the graph of the inverse variation.
4) y 
2
x
Sketch the asymptotes (both vertical and horizontal) and the graph of each equation.
Include a table.
5) y 
3
4
x 1
6) y 
1
2
x3
Write an equation for each translation of y 
7)
a) x = 2 and y = -9
4
that has the given asymptotes.
x
b) x = -3 and y = 8
Describe the vertical asymptotes and holes for the graph of each rational function.
Remember to write your answer for both as x =
5
8) y 
x4
x 2  8x  7
10) y  2
x  x  42
x9
9) y  2
x  x  42
Find the horizontal asymptote of the graph of each function. Write your answer as y =
11) y 
18 x  11
6 x  13
12) y 
32 x 3  5
8 x 6  17
Sketch the graph of the rational function. Use the graphing calculator and include a table.
No crappy graphs!!
13) y 
x4
x  x2
2
Simplify each rational expression. State any restrictions on the variables.
24 x10 y 4
14)
42 xy 6
3 x  15
15) 2
x  9 x  20
x 2  16
16) 2
x  6x  8
Multiply and simplify. State any restrictions on the variables.
4m 3 10n 4
17)

9n 5 2m
19)
x 2  2 x  35 x  6
18)

x 2  36
x  7 2
x 2  4x x 2  1

x 2  6x  5 x3
Divide and simplify.
20)
5 y  10
6 y  12
 2
y 8
y  10 y  16
21)
x 2  3x  28
x 2  16

x 2  9 x  14 x 2  6 x  8
Add or Subtract and Simplify
22)
4
5

x 1 x  6
23)
8
3
 2
x  3x  4 x  7 x  12
24)
2x
4

2
3y
8 xy 3
25)
10 x
4

x  2 x  24 x  6
2
2
Simplify each complex fraction.
10 
26)
3
x
9
5
x
3
4
27)
1
3
6
4
Solve each equation. Don’t forget to check each solution!
28)
2
6

x7 x4
29)
x4
5

2
x5
6
1
x
31)
1 x
7


3 12 4 x
30) x 
32)
6
4
3


x  8 x  15 x  3 x  5
2
Bonus Problems (1 point each)
Write the function that models the variation. Find z when x = 8 and y = 12
33) z varies jointly with x and y and z = 84 when x = 3 and y = 4
Find any points of discontinuity for each rational function below.
x3
34) y  3
3 x  9 x 2  120 x
35) y 
2 x  32
6 x 2  x  15