Question

Use graphs and tables to find the limit and identify any vertical asymptotes of the function.

Answer 1

Lim x→8- [1/(x-8)]=1/(8-8)=1/(-0)→Lim x→8- [1/(x-8)]=-Infinite

Vertical asymptote: x=8

Answer 2

Answer:

The limit of the function is $lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty$ and the vertical asymptotes is x=8.

Step-by-step explanation:

The given function is

$f(x)=\frac{1}{x-8}$

We need to find the value of

$lim_{x\rightarrow 8^-}\frac{1}{x-8}$

The graph of the function f(x) is attached below.

From the graph it is clear that the function approaches to -∞ as x approaches to 8 from left. So, by the graph we can say that

$lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty$

The table of values is attached below. From the table it is clear that the value of f(x) decreasing as the value of x is closed to 8 from left. So, by the table we can say that

$lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty$

To find the vertical asymptotes equate denominator, equal to 0.

$x-8=0$

$x=8$

Therefore the limit of the function is $lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty$ and the vertical asymptotes is x=8.