Question

Does the graph of the function f(x) = x^2 − 8x − 9 / x + 1 have a vertical asymptote or a point missing at x = −1? Explain
your reasoning, and support your answer numerically.

Answer 1

Answer:

Yes, the graph of the function has vertical asymptote at x=-1.

Step-by-step explanation:

Given : Function $f(x)=\frac{x^2-8x-9}{x+1}$

To find : Does the graph of the function have a vertical asymptote or a point missing at x = −1?

Solution :

The vertical asymptote of the rational function is when we put denominator equals to zero.

In the function $f(x)=\frac{x^2-8x-9}{x+1}$

Denominator - $x+1$

Vertical asymptote is at $x+1=0\Rightarrow x=-1$

Yes, the graph of the function has vertical asymptote at x=-1.