review- rational fxs.tst - tperry-math

#_______Name___________________________________Subj______________Per_______Date_________________________
Review: Rational Functions
a) Use the RATEY method to graph the function. Be
sure to label critical information on the graph.
b) Then, state the domain and range.
2
1) f(x) =
(5 + x)2
3) f(x) =
x2 - 2x - 15
x-2
y
y
x
x
4) R(x) =
2) f(x) =
x2 + 10x + 25
x2 - 5
x2 + x - 12
x2 - x - 20
y
y
x
x
1
Solve the problem.
5) Decide which of the rational functions might
have the given graph.
12)
2x
≥ 2x
6-x
13)
18
15
>
x-5
x-1
y
5
-5
Solve the problem.
14) A lens can be used to create an image of an
object on the opposite side of the lens, such
as the image created on a movie screen. Every
lens has a measurement called its focal
length, f. The distance s1 of the object to the
lens is related to the distance s2 of the lens to
the image by the function
fs2
s1 =
.
s2 - f
x
5
-5
6) Decide which of the rational functions might
have the given graph.
5
For a lens with f = 0.3 m, what are the
asymptotes of this function?
y
15) A rare species of insect was discovered in the
rain forest of Costa Rica. Environmentalists
transplant the insect into a protected area.
The population of the insect t months after
being transplanted is
45(1 + 0.6t)
.
P(t) =
(3 + 0.02t)
4
3
2
1
-5
-4
-3
-2
-1
1
2
3
4
5 x
-1
a) What was the population when t = 0?
b) What will the population be after 10
years?
c) What is the largest value the population
could reach?
-2
-3
-4
-5
16) Economists use what is called a Leffer curve to
predict the government revenue for tax rates
from 0% to 100%. Economists agree that the
end points of the curve generate 0 revenue,
but disagree on the tax rate that produces the
maximum revenue. Suppose an economist
produces this rational function
10x(100 - x)
R(x) =
, where R is revenue
15 + x
Solve the equation.
6
4
7)
=
2x - 3
2x + 5
8)
1
1
x-6
+
=
x
x-7
x-7
9)
2x
3
4
=
x2 - 4
x2 - 4 x + 2
10)
in millions at a tax rate of x percent. Use a
graphing calculator to graph the function.
What tax rate produces the maximum
revenue? What is the maximum revenue?
1
-1
7
=
x-7
x - 14 x2 - 21x + 98
Solve the inequality. Then, graph the solution.
x-1
11)
<1
x+2
2

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