Name:_________________________________
Date:__________ Period:__________
Algebra 2 Ch.9 Test Review
1. Write a function that models the variation. Solve for K and write the general formula.
x = 10 when y  15 when z  2 , z varies directly with x and inversely with y.
Is the relationship between the values in each table a direct variation, an inverse variation, or neither?
Write an equation to model any direct or inverse variation.
2.
X
Y
3.
3
24
4
18
8
9
Write an equation for the translation of y 
4. x  2, y  2
X
Y
11
15
3
with the given asymptotes.
x
5. x  4, y  5
13
13
15
11
Name:_________________________________
Date:__________ Period:__________
For each rational function, identify any holes or horizontal or vertical asymptotes of its graph.
2
( x  1)
x6
6. y 
7. y 
8. y 
x7
( x  2)( x  1)
( x  4)( x  5)
Sketch the graph of each rational function. Don’t forget the Horizontal and Vertical Asymptotes.
1
2
2
9. y 
10. y 
x3
( x  3)
5
5
4
4
3
3
2
2
1
1
-7 -6 -5 -4 -3 -2 -1
-1
1 2 3 4 5 6 7
-7 -6 -5 -4 -3 -2 -1
-1
-2
-2
-3
-3
-4
-4
-5
-5
1 2 3 4 5 6 7
Simplify each rational expression. State any restrictions.
2y  4
2y
x2 1
x
11. 2
12. 2
y  2 y  8 2 y  4 y 2
x  5x  6
Name:_________________________________
Date:__________ Period:__________
Find the least common multiple of each pair of polynomials.
13. x 2  9 and (3x  5)( x  3) 2
14. 5( x  3)( x  1) and 2( x  1)( x  3)
Simplify each sum or difference.
2
x

15.
x  3 x 1
Solve each equation. Check each solution.
x x 1
17. 
2
4
19.
x 4x  6

5
 10
16.
x  2 x  11

x2  4
x2
18.
3x
1
x 1
20.
4x  8
0
x6
Name:_________________________________
Key:
3x
y
1.
k = 3 and z 
2.
Inverse y = 72/x
3.
Neither
4.
y
5.
3
y
5
( x  4)
3
2
( x  2)
Date:__________ Period:__________
11.
( x  1)
x  1 or -6
( x  6)
12.
1
2
y  ,0,2
2
( y  4)(1  2 y )
13.
( x  3) 2 ( x  3)(3x  5)
14.
10(x + 3)(x + 1)(x – 3)
15.
x 2  1x  2
x 2  2 x  3
6.
Vert. Asymp. x = -7
Horzt. Asymp. y = 0
16.
 9 x 2  4 x  44
x 4  4 x 2
7.
Hole x = 1
Vert. Asymp. x = -2
Horzt. Asymp. y = 0
17.
x=1
18.
x=½
Vert. Asymp. x = 4 and x = 5
Horzt. Asymp. y = 0
19.
x = -1
20.
x=2
8.
9.
10.