Problem Sheet #9 (3.5-3.7)
ClassID: _____ Name: _________________________ Hmk. 9 Score _________
Math 1090 – 001 Spring 2013
Instructor: Katrina Johnson
Complete each problem. Clearly indicate your final answer. No credit will be given without
supporting work.
1. Given the function f (x) =
3x 2 −11x − 4
2x 2 − 8
a) What is the domain of f? Write your answer in interval notation.
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b) Identify any vertical asymptote(s).
c) Identify the horizontal asymptote, if
any.
d) What are the x-intercept(s)?
e) What is the y-intercept?
f) Describe the end behavior of f.
2. Given f (x) = 2x − 6 , g(x) =
a) Find ( fh)(x) .
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3x
x +2
, and h(x) = 2
x − 25
x + 3x −10
b) Find (g − h)(x) .
2
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⎛ f ⎞
⎟(1)
⎝ g ⎠
d) Find ⎜
c) Find (g  f )(x)
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3. Identify the base function and describe the transformations. Then sketch the
transformed function, labeling at least three points.
a) f (x) = − x + 3 + 5
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Base function is y=_______
Transformation(s):
b) g(x) = 3x 2 −12x + 7
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Base function is y=_______
Transformation(s):
c) h(x) = 12 − 4 x − 3
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Base function is y=_______
Transformation(s):