7
QuizMultiple Choice

Vertical Asymptotes of Rational Functions — Quiz

Question 7 • Mathematics III

Which statement is true about the discontinuities of the function f of x ? f of x is equal to the fraction with numerator x minus 5 and denominator 3 x squared minus 17 x minus 28

Answer
A
There are asymptotes at x is equal to negative 7 and x is equal to 4 thirds .
B
There are asymptotes at x is equal to 7 and x is equal to negative 4 thirds .
C
There are holes at open paren negative 7 comma 0 close paren and x is equal to 4 thirds .
D
There are holes at x is equal to 7 and x is equal to negative 4 thirds .

Explanation

Factor the denominator: 3x² − 17x − 28 = (x − 7)(3x + 4). The denominator is zero at x = 7 and x = −4/3, and neither factor cancels with the numerator x − 5. Therefore, both discontinuities are vertical asymptotes, as stated in choice B.

AI-written and checked against the verified answer.

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