Question

move at least one of the 3 guide points below to complete the graph of $y = \sqrt{x - 2}$. 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 parent function shift

The parent function is $y=\sqrt{x}$, which has a domain $x\geq0$. For $y=\sqrt{x-2}$, this is a horizontal shift right by 2 units. The starting point (blue point) of $y=\sqrt{x}$ is $(0,0)$, so the new starting point is $(0+2, 0)=(2,0)$.

Step2: Find first red point

Choose $x=3$: $y=\sqrt{3-2}=\sqrt{1}=1$. So the point is $(3,1)$.

Step3: Find second red point

Choose $x=6$: $y=\sqrt{6-2}=\sqrt{4}=2$. So the point is $(6,2)$.

Answer:

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

The graph will now correctly represent $y=\sqrt{x-2}$.