Simplify f(x)and find any vertical asymptotes. $f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }$
A)f(x)= x - 4;no vertical asymptotes
B)f(x)= -x - 4;no vertical asymptotes
C)f(x)= x;no vertical asymptotes
D)f(x)= x + 4;no vertical asymptotes
E)f(x)= -x + 4;no vertical asymptotes

Question

Simplify f(x)and find any vertical asymptotes.​ $f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }$ ​
A)f(x)= x ​- 4;no vertical asymptotes
B)f(x)= -x ​- 4;no vertical asymptotes
C)f(x)= x;no vertical asymptotes
D)f(x)= x​ + 4;no vertical asymptotes
E)f(x)= -x ​+ 4;no vertical asymptotes

Quizplus · Accepted Answer

The function can be simplified by factoring the numerator as $f(x) = \frac{(x-4)(x+4)}{x+4}$, which simplifies to $f(x) = x - 4$ when $x \neq -4$. The point $x = -4$ is not a vertical asymptote but a point of removable discontinuity, leaving no vertical asymptotes.

Simplify F(x)and Find Any Vertical Asymptotes f(x)=x2−16x+4f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }f(x)=x+4x2−16​

Simplify F(x)and Find Any Vertical Asymptotes $f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }$