Graphs of Rational Functions Answers

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3

What is the oblique asymptote of ?

Question illustration
A
y = x + 5
B
y = x – 5
C
y = 5x
D
y = –5x
4

Determine the domain of the function .

Question illustration
A
(–1, 5)
B
(5, 5)
C
(–∞, –1) U (–1, 5) U (5, ∞)
D
(–∞, –5) U (–5, 5) U (5, ∞)
5

Consider the function . Which statement correctly describes the function’s behavior around its vertical asymptote?

Question illustration
A
As x → –2–, f(x) → ∞ and as x → –2+, f(x) → ∞.
B
As x → –2–, f(x) → –∞ and as x → –2+, f(x) → ∞.
C
As x → –2–, f(x) → –∞ and as x → –2+, f(x) → –∞.
D
As x → –2–, f(x) → ∞ and as x → –2+, f(x) → –∞.
6

Which statements describe the function ? Check all that apply. f(x) has a vertical asymptote at x = 8.f(x) has a vertical asymptote at x = 12.f(x) has a hole at x = –12.f(x) has a horizontal asymptote at y = 0. f(x) has an x-intercept at (–24, 0). f(x) is increasing from (8, ∞).

Question illustration
A
f(x) has a vertical asymptote at x = 8.
B
f(x) has a vertical asymptote at x = 12.
C
f(x) has a hole at x = –12.
D
f(x) has a horizontal asymptote at y = 0.
E
f(x) has an x-intercept at (–24, 0).
F
f(x) is increasing from (8, ∞).
10

Which statements describe the function ? Check all that apply.f(x) has one real zero because it crosses the x-axis once.f(x) has two real zeros because it crosses the x-axis twice.f(x) has real zeros at 1 and –1.f(x) has a real zero at 2.5.f(x) has x-intercepts at (1, 0) and (–1, 0).f(x) crosses the x-axis when x = 1 and x = –1.f(x) has an x-intercept at (2.5, 0).

Question illustration
A
f(x) has one real zero because it crosses the x-axis once.
B
f(x) has two real zeros because it crosses the x-axis twice.
C
f(x) has real zeros at 1 and –1.
D
f(x) has a real zero at 2.5.
E
f(x) has x-intercepts at (1, 0) and (–1, 0).
F
f(x) crosses the x-axis when x = 1 and x = –1.
G
f(x) has an x-intercept at (2.5, 0).

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