8
lesson pretestMultiple Choice

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Question 8 • Math 3

Which function has no horizontal asymptote?

Answer
A
f of x is equal to the fraction with numerator 2 x squared and denominator 3 x minus 1
B
f of x is equal to the fraction with numerator x minus 1 and denominator 3 x
C
f of x is equal to the fraction with numerator 3 x squared and denominator x squared minus 1
D
f of x is equal to the fraction with numerator 2 x minus 1 and denominator 3 x squared

Explanation

For a rational function, compare the degrees of the numerator and denominator. If the numerator’s degree is larger, the function has no horizontal asymptote. In A, the numerator has degree 2 and the denominator has degree 1, so there is no horizontal asymptote. In B, C, and D, the numerator’s degree is no greater than the denominator’s, so each has a horizontal asymptote.

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