College Algebra Quiz
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FUNCTIONS & GRAPHS
Question 1
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A student claims that the function
h
(
x
)
=
2
x
2
−
5
x
+
3
4
x
2
+
1
h(x) = \frac{2x^2 - 5x + 3}{4x^2 + 1}
h
(
x
)
=
4
x
2
+
1
2
x
2
−
5
x
+
3
has the same end behavior as
y
=
1
2
y = \frac{1}{2}
y
=
2
1
. Which statement best evaluates this claim?
A
The student is correct; both numerator and denominator have degree 2, so the end behavior approaches
2
4
=
1
2
\frac{2}{4} = \frac{1}{2}
4
2
=
2
1
B
The student is incorrect; the function has vertical asymptotes that affect the end behavior significantly
C
The student is incorrect; the end behavior approaches
y
=
2
y = 2
y
=
2
because the leading coefficient of the numerator is 2
D
The student is incorrect; since the denominator has a constant term, the horizontal asymptote is at
y
=
0
y = 0
y
=
0
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