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Byju's Answer
Standard XII
Mathematics
Skew Symmetric Matrix
Write a ratio...
Question
Write a rational function
f
with a slant asymptote
y
=
x
+
4
, a vertical asymptote at
x
=
5
and one of the zeros at
x
=
2
.
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Solution
vertical asymptote, the denominator must contain
(
x
−
5
)
and for zeros the numerator must contain
(
x
−
2
)
So far
f
(
x
)
=
x
−
2
x
−
5
For slant asymptote, quotient of numerator divided by denominator must be
(
x
+
4
)
Therefore:
f
(
x
)
=
(
x
+
4
)
(
x
−
2
)
x
−
5
So
f
(
x
)
=
x
2
+
2
x
−
8
x
−
5
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