Question

move at least one of the 3 guide points below to complete the graph of $y = \frac{3}{2}\sqrt{x}$. 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.
reset reflect over x-axis

Explanation:

Step1: Identify base function points

The base function is $y=\sqrt{x}$. Key points are $(0,0)$, $(1,1)$, $(4,2)$.

Step2: Apply vertical stretch factor

Multiply y-values by $\frac{3}{2}$:

• For $(0,0)$: $y=\frac{3}{2}\times0=0$ → $(0,0)$
• For $(1,1)$: $y=\frac{3}{2}\times1=\frac{3}{2}=1.5$ → $(1, 1.5)$
• For $(4,2)$: $y=\frac{3}{2}\times2=3$ → $(4, 3)$

Step3: Adjust the guide points

Move the blue point (origin) to $(0,0)$ (if not already there). Move the first red point from $(1,1)$ to $(1, 1.5)$. Move the second red point from $(4,2)$ to $(4, 3)$.

Answer:

1. Keep the blue point at $(0,0)$.
2. Move the red point at $(1,1)$ to $(1, 1.5)$.
3. Move the red point at $(4,2)$ to $(4, 3)$.

This will form the correct graph of $y=\frac{3}{2}\sqrt{x}$.