Provide an appropriate response.
-Which function has no vertical asymptote? Why? a. $f ( x ) = \frac { x - 4 } { x ^ { 2 } - 9 }$
b. $f ( x ) = \frac { 2 } { x ^ { 2 } - 6 x }$
c. $f ( x ) = \frac { 3 x ^ { 2 } + 15 } { x ^ { 2 } + 6 }$
d. $f ( x ) = \frac { x + 5 } { ( x - 5 ) ( x - 3 ) }$
A) b. The numerator is never equal to 0.
B) d. No factor from the denominator cancels out.
C) a. The degree of the denominator is larger than the degree of the numerator.
D) c. The denominator is never equal to 0.

Question

Quizplus · Accepted Answer

The function $f(x) = \frac{3x^2 + 15}{x^2 + 6}$ has no vertical asymptote because the denominator $x^2 + 6$ cannot be zero for any real value of $x$, as $x^2$ is always non-negative and adding 6 ensures the denominator is always positive.

Provide an Appropriate Response f(x)=x−4x2−9f ( x ) = \frac { x - 4 } { x ^ { 2 } - 9 }f(x)=x2−9x−4​

Provide an Appropriate Response $f ( x ) = \frac { x - 4 } { x ^ { 2 } - 9 }$