Chapter 1, Problem 16RE

To determine

To check: Whether the graph of the function $y=x^{\frac{2}{5}}$ is symmetric about the y-axis, the origin or neither.

Answer to Problem 16RE

The graph of function $y=x^{\frac{2}{5}}$ is symmetric about the $y$ -axis.

Explanation of Solution

Given information:The given function is $y=x^{\frac{2}{5}}$ .

To graph a function $y=x^{\frac{2}{5}}$ , follow the steps using graphing calculator.

First press “ON” button on graphical calculator, press $\boxed{\text{Y}=}$ key and enter right hand side of the equation $y=x^{\frac{2}{5}}$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{\text{X}}\boxed{^}\boxed{(}\boxed{2}\boxed{÷}\boxed{5}\boxed{)}$ .

The display will show the equation,

  ${\text{Y}}_{\text{1}}=\text{X}^\left(2/5\right)$

Now, press the $\boxed{\text{GRAPH}}$ key and $\boxed{\text{TRACE}}$ key to produce the graph of both the equations as shown below.

  

Figure (1)

As observed from the graph, the function $y=x^{\frac{2}{5}}$ is symmetric about $y$ -axis.

Therefore, the graph of function $y=x^{\frac{2}{5}}$ is symmetric about the $y$ -axis.