10
QuizMultiple Choice

Rational Functions — Test

Question 10 • Precalculus

Which statement is true about the discontinuities of the function f of x ? f of x is equal to the fraction with numerator x plus 1 and denominator 6 x squared minus 7 x minus 3

Answer
A
There are asymptotes at x is equal to negative 3 halves and x is equal to 1 third .
B
There are holes at x is equal to 3 halves and x is equal to negative 1 third .
C
There are asymptotes at x is equal to 3 halves and x is equal to negative 1 third .
D
There are holes at x is equal to negative 3 halves and x is equal to 1 third .

Explanation

Factor the denominator: 6x² − 7x − 3 = (3x + 1)(2x − 3). It is zero at x = −1/3 and x = 3/2. Neither factor cancels with the numerator x + 1, so these discontinuities are vertical asymptotes, not holes. The correct statement is that there are asymptotes at x = 3/2 and x = −1/3.

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