Q. 32 - Precalculus Enhanced with Graphing Utilities

Question

If $(3,6)$ is a point on the graph of $y=f\left(x\right)$, which of the following points must be on the graph of$y=f(-x)$?

Step-by-Step Solution

Answer

The point$(-3,6)$ lies on the graph of $y=f(-x)$so the option d is correct

Step 1. Given data

The point $(3,6)$lies on the graph of the function$y=f\left(x\right)$

transformed function is$y=f(-x)$

Step 2. Explanation of correct option D

Point$(3,6)$ lies on $y=f\left(x\right)$

so $f\left(3\right)=6$

$y=f(-x)$is a reflection of $y=f\left(x\right)$about y-axis

so y coordinate of $y=f(-x)$at $x=-3$

$$\begin{gathered} y=f(-x) \\ y=f(-(-3\left)\right) \\ y=f\left(3\right) \\ y=6 \end{gathered}$$

point $(-3,6)$ lies on$y=f(-x)$ so option d is correct.

Step 3. explanation of incorrect options

• $y=f(-x)$is a reflection of$y=f\left(x\right)$ about y-axis so the point$(-3,6)$ will lie on$y=f(-x)$, not $(3,6)$ and option a is incorrect
• $y=f(-x)$ is a reflection of$y=f\left(x\right)$ about y-axis so the point$(-3,6)$ will lie on$y=f(-x)$, not $(6,-3)$and option b is incorrect 
• $y=f(-x)$ is a reflection of$y=f\left(x\right)$ about y-axis so the point $(-3,6)$ will lie on$y=f(-x)$, not $(3,-6)$and option c is incorrect