Question

What is the end behavior of f(x) in the function f(x) = log(x - 2) as x approaches 2?

Answer 1

Step 1

Given; What is the end behavior of f(x) in the function f(x) = log(x - 2) as x approaches 2?

Step 2

Graph the function

$\begin{gathered} \lim _{x\to \:2}\left(\ln \left(x-2\right)\right) \\ \mathrm{If\:}\lim _{x\to a-}f\left(x\right)\ne \lim _{x\to a+}f\left(x\right)\mathrm{\:then\:the\:limit\:does\:not\:exist} \\ \end{gathered}$

Thus;

$\lim _{x\to \:2}\left(\ln \left(x-2\right)\right)=\mathrm{Does\:not\:exist}$

Therefore the answer is;

$f(x)\rightarrow-\infty$