Chapter 1.4, Problem 67E

To determine

To find if the given statement is true or false.

Answer to Problem 67E

False

Explanation of Solution

Given:

The given statement says that “The graph of $y=f(-x)$ is a reflection of the graph of $y=f(x)$ in the $x$ axis”.

From the statement, it can be understood that for every point $(x,y)$ on the right side of the $x$ axis, there is a point $(-x,y)$ equidistant to the left of the $x$ axis.

But when the points are plotted, for every point $(x,y)$ on the right side of the $y$ axis, there is a point $(-x,y)$ equidistant to the left of the $y$ axis as shown in the example below:

Let $f(x)={(x-4)}^2$ and $f(-x)={(-x-4)}^2$ represented by the red and blue lines respectively.

  

The points that are equidistant about $y$ axis are as shown below:

  

Therefore, the given statement is false since the points are equidistant about the $y$ axis.