Rational Functions and Vertical Asymptotes
AP Precalculus · Flashcards
AP PRECALCULUS · FLASHCARDS
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QUESTION
Determine the vertical asymptote for
f
(
x
)
=
x
x
2
+
4
x
+
4
f(x) = \frac{x}{x^2 + 4x + 4}
f
(
x
)
=
x
2
+
4
x
+
4
x
.
QUESTION
Identify the vertical asymptote of
f
(
x
)
=
1
x
−
3
f(x) = \frac{1}{x - 3}
f
(
x
)
=
x
−
3
1
.
QUESTION
What condition creates a vertical asymptote in a rational function?
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ANSWER
A vertical asymptote occurs where
Q
(
x
)
=
0
Q(x) = 0
Q
(
x
)
=
0
and
P
(
x
)
≠
0
P(x) \neq 0
P
(
x
)
=
0
. Denominator zero with nonzero numerator creates infinite discontinuity.
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