Question

Determine whether the function fis even, odd, or neither. If fis even or odd, use symmetry to sketch its graph.

$f\left(x\right)=x^2+x$

Short answer

The function$f\left(x\right)=x^2+x$ is neither even or odd.

Step-by-step solution

Step 1. Definition of even function.

A function f is said to be even if$f(-x)=f\left(x\right)$ for all x in the domain of f.

The graph of even function is symmetric with respect to y-axis.

Step 2. Definition of odd function.

A function f is said to be odd if$f(-x)=f\left(x\right)$ for all x in the domain of f.

The graph of odd function is symmetric with respect to x-axis.

Step 3. Determining whether the function is even or odd.

Given function is

$$\begin{gathered} f\left(x\right)=x^2+x \\ f(-x)=(-x^2)+(-x) \\ =x^2-x \end{gathered}$$

As we see width="214" height="21" role="math">f(-x)≠f(x)orf(-x)≠-f(x)

So, the function is neither even or odd.

Thus, the graph is