Q. 23 - Precalculus Enhanced with Graphing Utilities

Question

Write the function whose graph is the graph of $y=x^3$, but is:

Reflected about the $y$-axis.

Step-by-Step Solution

Answer

The function is $y=-x^3$

Step 1. Given information

The given function is $y=x^3$

Step 2. Find the function for reflected about the y -axis.

For a function $y=f\left(x\right)$, the reflection about the $y$-axis of the graph of the function is given by $y=f(-x)$.

So substitute $-x$ in place of $x$ in the given function,

$$\begin{gathered} y={(-x)}^3 \\ y=-x^3 \end{gathered}$$

Therefore, the new function is $y=-x^3$