Question

Determine the vertical asymptote(s) of the given function. If none exists, state that fact. f(x)=x2+5x+4−x2+16

A) x=−1,x=−4
B) x=−1
C) x=−1,x=4
D) x=1,x=−4

Answer 1

Upon simplifying the given function f(x), it becomes clear that it is a linear function, which means it does not have any vertical asymptotes.

Step-by-step explanation:

To determine the vertical asymptote(s) of the function f(x) = x² + 5x + 4 − x² + 16, we first simplify the function by combining like terms.

Here's the simplification process:

x² + 5x + 4 − x² + 16 simplifies to 5x + 20 because x² − x² equals 0.The remaining expression is 5x + 20.Divide the whole expression by 5 to get x + 4.This is a linear function and does not have any vertical asymptotes.

Therefore, the correct answer is that there are no vertical asymptotes for this function.