Question

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

Answer 1

Answer:

The line x = 8 is our vertical asymptote

The limit of $\frac{1}{x-8}$ as x approaches 8 from the left is negative infinity; -∞

Step-by-step explanation:

We have been given the following function;

$\frac{1}{x-8}$

Considering that the function is rational, it will defined everywhere on the real line except where the expression in the denominator will be 0;

That is the function will not be defined where;

x - 8 = 0

solving for x yields;

x = 8

The function will be approaching the vertical line x = 8 asymptotically, meaning that the function will never touch or cross this line. We can therefore say that,

The line x = 8 is our vertical asymptote for the given function

The limit of $\frac{1}{x-8}$ as x approaches 8 from the left;

$\lim_{x \to8^{-} }\frac{1}{x-8}$

For x approaching 8 from the left, $x$ which implies that $x-8$

The denominator will be a negative quantity approaching 0 from the left, that is -∞.

Thus;

$\lim_{x \to8^{-} }\frac{1}{x-8}$ = -∞

Find the graph attached.