Question

move at least one of the 3 guide points below to complete the graph of $y = 3\sqrt{x}$. moving the red points changes the vertical stretch or compression. moving the blue point shifts the function left/right/up/down. click the buttons below to start over or reflect over the x - axis.

Explanation:

Step1: Identify base function points

The base function is $y=\sqrt{x}$. Key points:

• When $x=0$, $y=\sqrt{0}=0$ → $(0,0)$
• When $x=1$, $y=\sqrt{1}=1$ → $(1,1)$
• When $x=4$, $y=\sqrt{4}=2$ → $(4,2)$

Step2: Apply vertical stretch factor

For $y=3\sqrt{x}$, multiply each $y$-value by 3:

• $(0, 3\times0)=(0,0)$
• $(1, 3\times1)=(1,3)$
• $(4, 3\times2)=(4,6)$

Step3: Adjust guide points

Move the red point at $(1,1)$ to $(1,3)$, and the red point at $(4,2)$ to $(4,6)$. The blue point at $(0,0)$ stays unchanged.

Answer:

1. Keep the blue point at $(0, 0)$.
2. Move the first red point from $(1,1)$ to $(1, 3)$.
3. Move the second red point from $(4,2)$ to $(4, 6)$.

The resulting curve will be the graph of $y=3\sqrt{x}$.