Section 4.5 Extra Practice
STUDENT BOOK PAGES 207–214
1. Determine which of the following functions has
vertical asymptotes. State the equations of these
asymptotes if they exist.
2x ⫹ 1
a. f (x) ⫽ 2
x ⫺ x ⫺ 20
3x ⫺ 1
b. f (x) ⫽ 2
3x ⫹ 20x ⫺ 7
x⫺8
c. f (x) ⫽ 2
x ⫹ 16x ⫹ 64
2. For the following functions,
4. a. How many maximum and minimum values are
possible for a polynomial function of degree 2?
b. How many maximum and minimum values are
possible for a linear function? Explain your
reasoning.
5. How many points of inflection are possible for a
polynomial function of degree 2?
6. What is the equation of the oblique asymptote to the
x 2 ⫺ 3x ⫺ 4
graph of the function f (x) ⫽
x⫺1
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i. analyze f (x) by finding the domain, intercepts,
and asymptotes
ii. analyze f ⬘(x) by finding critical points, intervals
where f (x) is increasing and decreasing, and local
maxima and minima
iii. analyze f ⬙(x) by finding points of inflection and
intervals where the graph is concave up and
concave down
iv. sketch the graph of f (x)
a. x 3 ⫺ 4x 2 ⫹ x ⫺ 2
x
b. f (x) ⫽ 2
x ⫺ 16
3. Use the algorithm for curve sketching to sketch the
graph of each of the following functions.
a. f (x) ⫽ x 4 ⫺ 2x 3 ⫺ 4x 2
1
b. f (x) ⫽ 2
x ⫺ 9x
2
c. f (x) ⫽ (x ⫹ 4) 3
x⫺3
d. f (x) ⫽ 2
x ⫺4
Section 4.5 Extra Practice
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