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)\\e \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`