Chapter 1, Problem 18RE

To determine

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

Answer to Problem 18RE

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

Explanation of Solution

Given information:The given function is $y=e^{-x^2}$ .

To graph a function $y=e^{-x^2}$ , 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 $y=e^{-x^2}$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{2\text{nd}}\boxed{\text{LN}}\boxed{(-)}\boxed{\text{X}}\boxed{^}\boxed{2}\boxed{)}$ .

The display will show the equation,

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

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

  

Figure (1)

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

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