Rational Functions and Holes
AP Precalculus · Flashcards · Application
AP PRECALCULUS · FLASHCARDS
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QUESTION
State the horizontal asymptote of
f
(
x
)
=
2
x
x
2
+
1
f(x) = \frac{2x}{x^2 + 1}
f
(
x
)
=
x
2
+
1
2
x
.
QUESTION
Find the removable discontinuity of
f
(
x
)
=
x
2
−
9
x
−
3
f(x) = \frac{x^2 - 9}{x - 3}
f
(
x
)
=
x
−
3
x
2
−
9
.
QUESTION
Perform long division on
f
(
x
)
=
x
2
+
3
x
+
2
x
+
1
f(x) = \frac{x^2 + 3x + 2}{x + 1}
f
(
x
)
=
x
+
1
x
2
+
3
x
+
2
.
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ANSWER
Quotient is
x
+
2
x + 2
x
+
2
, remainder is 0.
x
2
+
3
x
+
2
=
(
x
+
1
)
(
x
+
2
)
x^2 + 3x + 2 = (x+1)(x+2)
x
2
+
3
x
+
2
=
(
x
+
1
)
(
x
+
2
)
divides evenly.
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