Rational Functions and End Behavior
AP Precalculus · Flashcards · Application
AP PRECALCULUS · FLASHCARDS
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QUESTION
What is the end behavior of
f
(
x
)
=
2
x
2
x
3
+
1
f(x) = \frac{2x^2}{x^3 + 1}
f
(
x
)
=
x
3
+
1
2
x
2
as
x
→
∞
x \to \infty
x
→
∞
?
QUESTION
State the vertical asymptotes for
f
(
x
)
=
x
2
−
1
x
2
−
4
f(x) = \frac{x^2-1}{x^2-4}
f
(
x
)
=
x
2
−
4
x
2
−
1
.
QUESTION
State the vertical asymptotes for
f
(
x
)
=
1
x
2
−
4
x
+
4
f(x) = \frac{1}{x^2 - 4x + 4}
f
(
x
)
=
x
2
−
4
x
+
4
1
.
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ANSWER
Vertical asymptote at
x
=
2
x = 2
x
=
2
. Perfect square:
(
x
−
2
)
2
=
0
(x-2)^2 = 0
(
x
−
2
)
2
=
0
gives
x
=
2
x = 2
x
=
2
.
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