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 $f(x) = \frac{x^2 - 16}{x + 4}$ can be simplified by factoring the numerator as a difference of squares: $x^2 - 16 = (x + 4)(x - 4)$. This gives $f(x) = \frac{(x + 4)(x - 4)}{x + 4}$. The $x + 4$ terms cancel out, leaving $f(x) = x - 4$. Since the cancellation removes the denominator, there are 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 $f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 }$