Q. 31 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

The point$(3,-6)$ lies on the graph $y=-f\left(x\right)$ so the option c 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$y=-f\left(x\right)$.

Step 2. Explanation of correct option C

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

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

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

so y coordinate of $y=-f\left(x\right)$ at $x=3$

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

point $(3,-6)$ lies on $y=-f\left(x\right)$ so option C is correct.

Step 3. explanation of incorrect options

• point$(6,-3)$does not lie on$y=f\left(x\right)$so$(6,3)$can not lie on $y=-f\left(x\right)$and option a is incorrect.
• point$\left(6,3\right)$does not lie on $y=f\left(x\right)$so$(6,-3)$can not lie on$y=-f\left(x\right)$and option b is incorrect.
• point$(-3,-6)$does not lie on$y=f\left(x\right)$so$(-3,6)$can not lie on$y=-f\left(x\right)$and option d is incorrect.