Question

question
graph the equation shown below by transforming the graph of the parent function.
( y = -sqrt{x} )

Explanation:

Step1: Identify parent function

Parent function is $y=\sqrt{x}$

Step2: List parent function points

For $x=0$: $y=\sqrt{0}=0$; $x=1$: $y=\sqrt{1}=1$; $x=4$: $y=\sqrt{4}=2$; $x=9$: $y=\sqrt{9}=3$
Points: $(0,0), (1,1), (4,2), (9,3)$

Step3: Apply reflection transformation

The function $y=-\sqrt{x}$ is a reflection of $y=\sqrt{x}$ over the x-axis. Multiply each y-coordinate by $-1$:
New points: $(0,0), (1,-1), (4,-2), (9,-3)$

Step4: Plot and connect points

Plot the transformed points and draw a smooth curve through them.

Answer:

The graph of $y=-\sqrt{x}$ is the reflection of $y=\sqrt{x}$ over the x-axis, passing through the points $(0,0)$, $(1,-1)$, $(4,-2)$, $(9,-3)$ with a smooth curve extending to the right.