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$y=f(-x)$?

Short answer

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

Step-by-step solution

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 dis 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 ais 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 bis incorrect
• role="math" localid="1645809944520" $y=f(-x)$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 optioncis incorrect