REVIEW FOR 8.1-8.3 TEST
Name: _________________________________________ Class Period: ______ Date: _________________________
Variation Formulas:
Direct Variation
Inverse Variation
y
k
x
xy  k
Write the equation that models the variation, then solve.
1.) If y varies directly with x and y = 8 when x = 2,
find y when x = 9.
2.) If y varies directly with x and y = 9 when x = 15,
find x when y = 21.
3.) If y varies inversely with x and y = 15 when x = 3,
find x when y = 9.
4.) If y varies inversely with x and y = 2 when x = 25,
find x when y = 40.
(Optional)
5.) Suppose y varies directly with x and inversely with z.
If y = 30 when x = 5 and z = 9, find x
when y = 3 and z = 2.
(Optional)
6.) Suppose z varies directly with x and inversely with y.
If y = 2 when z = 15 and x = 6, find z
when x = 4 and y = 8.
Matching. If z = 8 when x = 10 and y = 14, which function models the relationship in #7-10.
a)
𝑥𝑧
𝑦
=
40
7
b) 𝑥𝑦 = 140
_____ 7.) y varies directly with x.
c) 𝑦𝑧 = 112
d)
𝑦
𝑥
=
_____ 8.) y varies inversely with x.
_____ 9.) z varies directly with y and inversely with x. _____ 10.) y varies inversely with z.
7
5
Sketch, using a graphing calculator. Include the Vertical and Horizontal Asymptote on your Graph.
11.) f(x) =
2
𝑥+4
12.) f(x) =
−1
𝑥
y
y











x








1
3
13.) f(x) = 𝑥−2 + 3
14.) f(x) = 𝑥
y
y










x




17.) y =





(𝑥+3)(𝑥−4)
𝑥2 +𝑥−20
𝑥2 −12𝑥+35
𝑥−5


Find the vertical asymptotes and/or holes for the graph of each rational function.
15.) y =
x









16.) y =
18.) y =
𝑥−1
𝑥2 −𝑥−6
𝑥−3
𝑥+4


x

Sketch the graph of each rational function using a graphing calculator.
19.) f(x) =
2
20.) f(x) =
(𝑥−1)(𝑥+3)
𝑥 2 −3𝑥−10
𝑥−5
y
y


21.) f(x) =










x











𝑥+3
x


3
22.) f(x) =
𝑥−4

(𝑥−2)(𝑥+2)
y
y












x




𝑥 2 +𝑥−6
24.) f(x) =
𝑥+3







𝑥−2



3
y
y

x











23.) f(x) =



x










x
