Chapter 1, Problem 7RCC

To determine

To sketch: The rough graphs of the function $f\left(x\right)=x,g\left(x\right)=x^2,h\left(x\right)=x^3\text{ and }j\left(x\right)=x^4$ on the same axes.

Explanation of Solution

The rough graphs of the functions $f\left(x\right)=x,g\left(x\right)=x^2,h\left(x\right)=x^3\text{ and }j\left(x\right)=x^4$ are drawn and shown below in Figure 1.

From Figure 1, it is observed that the graphs of the functions $g\left(x\right)=x^2\text{ and }j\left(x\right)=x^4$ are symmetric about vertical axis. Therefore, the functions $g\left(x\right)\text{ and j}\left(x\right)$ are called even functions as they are symmetric about the origin.

Similarly, it is observed that the graphs of the functions $f\left(x\right)=x\text{and }h\left(x\right)=x^3$ are symmetric about vertical axis. Therefore, the functions $f\left(x\right)\text{ and }h\left(x\right)$ are called odd functions as they are symmetric about the origin.