Answer:
The limit of the function is [tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex] and the vertical asymptotes is x=8.
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{1}{x-8}[/tex]
We need to find the value of
[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}[/tex]
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
[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex]
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
[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex]
To find the vertical asymptotes equate denominator, equal to 0.
[tex]x-8=0[/tex]
[tex]x=8[/tex]
Therefore the limit of the function is [tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex] and the vertical asymptotes is x=8.
