Section 4.3 Extra Practice
STUDENT BOOK PAGES 181–195
x⫺1
1. For the function f (x) ⫽ x 2 ⫺ 1, determine the
vertical asymptote. Then, explain why x ⫽ 1 is not a
vertical asymptote.
2. State the equations of the vertical and horizontal
asymptotes of the curves shown.
a.
12
8
4
–12 –8 –4 0
–4
–8
–12
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b.
5. For each of the following functions, check for
discontinuities and find any asymptotes. Determine
the intercepts and then make a rough sketch of the
function.
x⫹5
a. f (x) ⫽
x⫺3
8
b. f (x) ⫽
(x ⫺ 4) 2
2x 2 ⫺ 9x ⫺ 5
c. f (x) ⫽
x⫺5
(3 ⫹ x)(2 ⫺ 3x)
d. f (x) ⫽
x 2 ⫺ 2x
y
x
4 8 12
10
8
6
4
2
–10 –8 –6 –4 –2 0
–2
–4
–6
–8
–10
4. Determine the equation of the oblique asymptote for
each of the following functions.
2x 2 ⫹ x
a. f (x) ⫽
x⫺3
6x 2 ⫺ 1
b. f (x) ⫽
2x ⫹ 4
y
ax ⫹ b
x
2 4 6 8 10
6. For the function f (x) ⫽ cx 2 ⫺ d , where a, b, c, d are
positive constants and a ⫽ 0, c ⫽ 0:
a. determine the horizontal asymptote of the graph
b. determine the vertical asymptotes of the graph
ax ⫹ 4
7. Find constants a and b that guarantee f (x) ⫽ 2 ⫺ bx
has a vertical asymptote at x ⫽ 23 and horizontal
asymptote at y ⫽ ⫺2.
3. For each of the following functions, determine the
equations of any vertical asymptotes and horizontal
asymptotes.
x
a. f (x) ⫽
x⫹2
x
b. f (x) ⫽ 2
x ⫹ 4x
x2 ⫹ 4
c. f (x) ⫽ 2
x ⫺4
5x 2 ⫺ 13x
d. f (x) ⫽
4x
Section 4.3 Extra Practice
375