Chapter 1.3, Problem 69E

To determine

Tograph:Graph the function using graphing utility.

Explanation of Solution

Given information:The given function is $f\left(x\right)=3x^3-2x$

Graph: Using graphing calculator the graph of the function is shown below

  

Interpretation:

A function $y=f\left(x\right)$ is said to be an even function if the graph of the function is symmetrical about y-axis. Algebraically, $y=f\left(x\right)$ is even if $f\left(-x\right)=f\left(x\right)$ for all x in the domain.

Similarly, a function $y=f\left(x\right)$ is said to be an odd function if the graph of the function is symmetrical about origin. Algebraically, $y=f\left(x\right)$ is even if $f\left(-x\right)=-f\left(x\right)$ for all x in the domain.

Here the graph of the function is symmetric about y-axis

Therefore, the given function is an even function.