Chapter ISG, Problem 9.2.13P

To determine

To find: If the parent quadratic function is an even function or an odd function.

Answer to Problem 9.2.13P

Parent quadratic function is an even function.

Explanation of Solution

Given information: Function is even if $f(-x)=f(x)$ and is odd if $f(-x)=-f(x)$ , for all $x$ in the domain of the function.

Parent quadratic function: $f(x)=x^2$

Putting a negative value in parent quadratic function results in the same output as corresponding positive value, in other words, for $f(x)=x^2$ , $f(-x)=f(x)$ . Because when a negative value is squared, it results in a positive value, on the other hand squaring a positive value also always returns a positive value.

But $f(-x)\ne -f(x)$ for $f(x)=x^2$ , proving by a counter-example,

  $\begin{array}{l}$ f(-4)={(-4)}^2$\\ =16\end{array}$

  $\begin{array}{l}$ -(f(4))=-{(4)}^2$\\ =-16\end{array}$

Clearly $16\ne -16$ .

Thus, parent quadratic function is an even function.