Determine which of the rational functions given below has the following feature(s).
-There is a "hole" in its graph at x = 3
A) $f ( x ) = \frac { x + 3 } { ( x + 9 ) ( x + 3 ) }$

B) $f ( x ) = \frac { 3 x - 1 } { x + 9 }$

C) $f ( x ) = \frac { ( x - 3 ) ( x + 9 ) } { ( x + 5 ) ( x - 3 ) }$

D) $f ( x ) = \frac { x + 9 } { x - 3 }$

Question

Determine which of the rational functions given below has the following feature(s).
-There is a "hole" in its graph at x = 3 
A) $f ( x ) = \frac { x + 3 } { ( x + 9 ) ( x + 3 ) }$

B) $f ( x ) = \frac { 3 x - 1 } { x + 9 }$

C) $f ( x ) = \frac { ( x - 3 ) ( x + 9 ) } { ( x + 5 ) ( x - 3 ) }$

D) $f ( x ) = \frac { x + 9 } { x - 3 }$

Quizplus · Accepted Answer

A "hole" in the graph of a rational function occurs at a value of x if that x-value is a factor in both the numerator and the denominator, and they cancel each other out. In option C, the factor $x - 3$ is present in both the numerator and the denominator, indicating a hole at $x = 3$ when they cancel each other out.

Determine Which of the Rational Functions Given Below Has the Following