Q. 113 - Precalculus Enhanced with Graphing Utilities

Question

In Problems 113–116, graph each function. Based on the graph, state the domain and the range and find any intercepts. 

$f\left(x\right)=\left\{\begin{array}{ll}\ln \left(-x\right)& if x<0\\ \ln x& if x>0.\end{array}\right.$

Step-by-Step Solution

Answer

Step 1. Given information

It is given that $f\left(x\right)=\left\{\begin{array}{ll}\ln \left(-x\right)& if x<0\\ \ln x& if x>0.\end{array}\right.$

Step 2. Graph the function

Step 3. Find domain and range and any intercept in the graph

The domain of the function $f\left(x\right)$ is $\left(\infty ,\infty \right)$ and the range of the $f\left(x\right)$ is $(\infty ,-\raisebox{1ex}{$7$}\!\left/ \!\raisebox{-1ex}{$2$}\right.]$ and the intercept of the graph $f\left(x\right)$ at $y$-axis and the point $\left(0,1\right)$ and $\left(0,-1\right).$