Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

True or False 

The graph of $y=-f\left(x\right)$ is the reflection about the $x$-axis of the graph of $y=f\left(x\right)$. 

Step-by-Step Solution

Answer

True

Step 1. Concept Used

When the right side of the function $y=f\left(x\right)$ is multiplied by $-1$, the graph of the new function $y=-f\left(x\right)$ is the reflection about the $x$-axis of the graph of the function $y=f\left(x\right)$. 

Step 2. Identify true or false

As $-1$ is multiplied to the right hand side of the function $y=f\left(x\right)$ to get the function $y=-f\left(x\right)$.

So the two functions are reflections of each other about the $x$-axis.

So the statement given is true.