Name:_________________________________
Date:__________ Period:__________
Algebra 2 Ch.9 Test
SHOW ALL OF YOUR WORK!!!!!!!!!
1. Write a function that models the variation. Solve for K and write the general formula.
x  3 when y  12 when z  2 , z varies directly with y and inversely with x.
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.
1
4
2
2
4
1
Write an equation for the translation of y 
4. x  1, y  1
X
Y
-2
-8
2
with the given asymptotes.
x
5. x  5, y  3
1
4
3
12
Name:_________________________________
Date:__________ Period:__________
For each rational function, identify any holes or horizontal or vertical asymptotes of its graph.
x
( x  3)
x5
6. y 
7. y 
8. y 
x3
( x  2)( x  3)
( x  2)( x  3)
Holes________________________ Holes________________________ Holes________________________
Horzt Asymp_________________
Horzt Asymp_________________
Horzt Asymp_________________
Vert Asymp__________________
Vert Asymp__________________
Vert Asymp__________________
Sketch the graph of each rational function. Don’t forget the Horizontal and Vertical Asymptotes.
(Make a table of values. You will not get credit unless you SHOW YOUR WORK!!!)
1
1
3
9. y 
10. y 
x4
( x  2)
5
5
4
4
3
3
2
2
1
1
-5 -4 -3 -2 -1
1
2
3
4
5
-5 -4 -3 -2 -1
1
-1
-1
-2
-2
-3
-3
-4
-4
-5
-5
Simplify each rational expression. (Factor and Cancel.) State any restrictions.
2 x  4 12 x  12
3x 2  12
x
11. 2
12.
3x  3
x5
x  x6
2
3
4
5
Name:_________________________________
Date:__________ Period:__________
Find the least common multiple of each pair of polynomials.
13. x 2  16 and 5x  20
14. 7( x  2)( x  5) and 2( x  5) 2
Simplify each sum or difference.
2
x

15.
x5 x5
Solve each equation. Check each solution.
y  3 y 1

17.
5
7
19.
x
2x

4
3
16.
3x
1
 2
x 4 x
18.
x
 2x  3
2
20.
2x  4
0
x5
2