Answer
The graph of the functions $f\left( x \right)=\frac{{{x}^{2}}-1}{x}$ , $f\left( x \right)=\frac{2{{x}^{2}}}{{{x}^{2}}+4}$ , $f\left( x \right)=\frac{1}{x-1}$ , $f\left( x \right)=\frac{1}{{{\left( x+2 \right)}^{2}}}$ , and $f\left( x \right)=\frac{x+2}{{{x}^{2}}+x-6}$ are shown below.
Work Step by Step
It can be seen from the handmade graphs and the graphs obtained from the graphing utility that the graphs are the same. Hence, it is verified.
