Algebra 2H B
Chapter 8 Review
Name:______________________________
1. Suppose that x and y vary directly, and x = 2 when y = 8. Write the function that models the direct variation. Then find y
when x = -4.
2. Suppose that x and y vary inversely, and x = -13 when y = 100. Write the function that models the inverse variation. Then
find y when x = 7.
3. Suppose that z varies jointly with x and y and when x = 2 and y = 3, z = 60. Write the function that models each
variation. Find z when x = 4 and y = 9.
4. Suppose z varies directly with x and inversely with y and w, and when x = 8 and y = 2, z = 3 and w=4. Write the
function that models the variation. Find z when x = 6, y = 4 and w = 0.5.
Sketch the asymptotes and graph the function.
5. 𝑦 =
12
𝑥
6. 𝑦 = −
5
𝑥
3
7. Write an equation for the translation of 𝑦 = − 𝑥 that has the asymptotes x = -1 and y = 3.
5
8. Write an equation for the translation of 𝑦 = 𝑥 that has the asymptotes x = 6 and y = - 5.
Write an equation for the translation of y 
4
shown in each graph.
x
9.
10.
Find any points of discontinuity for the rational function. Label each as a hole or vertical asymptote.
11.
𝑦=
𝑥+5
𝑥−2
12.
𝑦=
(𝑥+6)
𝑥 2 +2𝑥−24
13.
𝑥−2
𝑦 = (𝑥+2)(𝑥−2)
𝑥
14.
𝑦=
18.
𝑦 = (𝑥+2)(𝑥−2)
𝑥(𝑥−1)
Find the horizontal asymptote of the rational function.
15.
𝑦=
3𝑥−12
𝑥 2 −2
16.
𝑦=
2𝑥 2 +3
𝑥 2 −6
17.
𝑦=
𝑥 2 +4𝑥+3
𝑥−7
𝑥−2
For each rational function, find all asymptotes, holes and intercepts. Then use a t-chart to find a few additional
points and graph.
3𝑥
𝑥+2
19.
𝑦=
20.
𝑦= 2
𝑥−2
𝑥 −4𝑥−12
 
























 
























Simplify.State any restrictions on the variable.
21.
𝑥 2 +3𝑥−18
𝑥 2 −36
22.
𝑥 2 +13𝑥+40
𝑥 2 −2𝑥−35
24.
y2  2 y
y 2  81

y 2  7 y  18 y 2  11y  18
25.
7 x4
21x

5
24 y
12 y 4
27.
y2  5 y  4
y2  9
 2
y2 1
y  5y  4
28.
3x3
x2  6 x  5

x 2  25
x2
23.
3x3 x 2  6 x  5

x 2  25
x2
26.
x2  4
x2  4x  4

x2  6x  9
x2  9
Simplify.
29.
y
2

y 1 y
x
2
 2
32. 2
x  5 x  6 x  3x  2
30.
33.
3
2
 2
x  2 x  7 x  10
1 3

2x x
4 7

3x x
Solve the equation. Check the solution.
35.
4
2
 1
x4 x
37.
1
5
1
 2

2 x  4 x  4 x 2
36.
4
3

x4 x2
38.
1
3
2

 2
x  5 5  x x  25
31.
x2
3

2
x 4 x2
34.
5
x3
1
2
x3