Question

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

$f\left(x\right)=x^4$

Short answer

The function $f\left(x\right)=x^4$ is even and hence the graph is symmetric with respect to y-axis.

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

$\begin{array}{c}f\left(x\right)=x^4\\ f(-x)=(-x^4)\\ =x^4\\ =f\left(x\right)\end{array}$

So, the function is even and hence the graph is symmetric with respect to y-axis

Thus, the graph is