Chapter 1, Problem 17RE

To determine

To check: Whether the graph of the function $y=x^2-2x-1$ is symmetric about the y -axis, the origin or neither.

Answer to Problem 17RE

The function $y=x^2-2x-1$ is neither symmetric about origin nor about $y$ -axis.

Explanation of Solution

Given information:The given function is $y=x^2-2x-1$ .

To graph a function $y=x^2-2x-1$ , 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 $y=x^2-2x-1$ after the symbol ${\text{Y}}_1$ . Enter the keystrokes $\boxed{\text{X}}\boxed{^}\boxed{2}\boxed{-}\boxed{2}\boxed{\text{X}}\boxed{-}\boxed{1}$ .

The display will show the equation,

  ${\text{Y}}_{\text{1}}=\text{X}^2-2\text{X}-1$

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 $y=x^2-2x-1$ is neither symmetric about origin nor about $y$ -axis.

Therefore, the function $y=x^2-2x-1$ is neither symmetric about origin nor about $y$ -axis.