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Algebra 2 Chapter 9 Review
1. Is the relationship between the values in the table a direct variation, an inverse variation, or neither? Write an
equation to model the direct and inverse variations.
x
3
5 8
24
y 20 12 7.5 2.5
2. Suppose that x and y vary inversely. Write a function that models the inverse variation and find the indicated
7
value.
Find y when x  4.
y  when x  2.
4
3. Write the function that models the relationship. Find y for the given values.
y varies jointly as w and x and inversely as z. y  – 40 when w  5, x  7, and z  – 7. Find y when w  5,
x  4, and z  2.
4. A drama club is planning a bus trip to New York City to see a Broadway play. The cost per person for the bus
rental varies inversely as the number of people going on the trip. It will cost $29 per person if 52 people go on
the trip. How much will it cost per person if 59 people go on the trip?
5. Find any points of discontinuity for the rational function and describe what they are.
x 1 x  2 x  3
y
x 1 x  2
b gb gb g
b gb g
6. Find the horizontal asymptote of the graph of the rational function.
2x
y
x9
7. Find any points of discontinuity for the rational function and describe what they are.
1
y 2
x  4x  3
8. Find the vertical and horizontal asymptotes, if any, of the graph of the rational function.
y
10
–10
10 x
–10
9. Sketch the graph of y 
x2
x3
10. Sketch the graph of y  
6
x 9
2
Multiply or Divide.
11.
5a 10a  10
5a  5
a
12.
x 2  3x  10
x2  5x  6

2 x 2  11x  5 2 x 2  7 x  3
13.
7 x4
21x

5
24 y 12 y 4
14.
x 2  2 x  1 x 2  3x  2
x2 1 x2  4x  4
2x
1
 2
x 9 x
Find each sum or difference.
15.
3
x

x4 x4
16.
17.
5
9
 2
x  36 x  5 x  6
18. 3 
2
2
1
x 5
2
Solve each equation.
19.
3x 5 x  1

4
3
21.
4
2
16

 2
x  3 x 1 x  2x  3
20.
2
5
6

 2
x 3 3 x x 9
Simplify.
2
22. x
3
y
1
23. x  2
1
2
x