Algebra 2 Quiz
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ANALYZE FUNCTIONS
Question 1
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Which rational function has a horizontal asymptote at
y
=
−
2
y = -2
y
=
−
2
and vertical asymptotes at
x
=
1
x = 1
x
=
1
and
x
=
−
4
x = -4
x
=
−
4
?
A
f
(
x
)
=
−
2
x
2
+
7
x
−
6
(
x
−
1
)
(
x
+
4
)
f(x) = \frac{-2x^2 + 7x - 6}{(x-1)(x+4)}
f
(
x
)
=
(
x
−
1
)
(
x
+
4
)
−
2
x
2
+
7
x
−
6
because this form clearly shows the desired asymptotic behavior
B
f
(
x
)
=
−
2
x
2
+
x
+
8
x
2
+
3
x
−
4
f(x) = \frac{-2x^2 + x + 8}{x^2 + 3x - 4}
f
(
x
)
=
x
2
+
3
x
−
4
−
2
x
2
+
x
+
8
because the denominator factors to
(
x
−
1
)
(
x
+
4
)
(x-1)(x+4)
(
x
−
1
)
(
x
+
4
)
giving the vertical asymptotes
C
f
(
x
)
=
−
2
x
2
+
5
x
−
3
x
2
+
3
x
−
4
f(x) = \frac{-2x^2 + 5x - 3}{x^2 + 3x - 4}
f
(
x
)
=
x
2
+
3
x
−
4
−
2
x
2
+
5
x
−
3
because the leading coefficient ratio gives the horizontal asymptote
D
f
(
x
)
=
−
2
x
3
+
5
x
2
−
3
x
x
2
+
3
x
−
4
f(x) = \frac{-2x^3 + 5x^2 - 3x}{x^2 + 3x - 4}
f
(
x
)
=
x
2
+
3
x
−
4
−
2
x
3
+
5
x
2
−
3
x
because higher degree numerator creates the horizontal asymptote
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