Chapter 2 - Section 2.6 - Rational Functions and Their Graphs - Exercise Set - Page 399: 67

The graph of the function is:

Work Step by Step

Substitute $x=-x$ , \begin{align} & f\left( x \right)=\frac{2}{{{x}^{2}}+x-2} \\ & f\left( -x \right)=\frac{2}{{{\left( -x \right)}^{2}}+\left( -x \right)-2} \\ & =\frac{2}{{{x}^{2}}-x-2} \end{align} Therefore, the function $f\left( -x \right)$ is not equal to $-f\left( x \right)$ and also $f\left( x \right)$. So, the graph of the function is neither symmetrical about the $y$-axis north the origin.

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