Question

move at least one of the 3 guide points below to complete the graph of $y = \sqrt{x} + 4$. 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 the parent function

The parent function is \( y = \sqrt{x} \), which has a vertex at \( (0, 0) \), and passes through \( (1, 1) \), \( (4, 2) \) etc.

Step2: Analyze the transformation

The given function is \( y = \sqrt{x} + 4 \), which is a vertical shift of the parent function \( y=\sqrt{x} \) by 4 units up. So the vertex (blue point) should be at \( (0, 4) \), the point at \( x = 1 \) (red point) should be at \( (1, \sqrt{1}+4)=(1, 5) \), and the point at \( x = 4 \) (red point) should be at \( (4, \sqrt{4}+4)=(4, 6) \).

Step3: Adjust the guide points

• Move the blue point (vertex) from \( (0, 0) \) to \( (0, 4) \).
• Move the red point at \( x = 1 \) from \( (1, 1) \) to \( (1, 5) \).
• Move the red point at \( x = 4 \) from \( (4, 2) \) to \( (4, 6) \).

After moving these points, the graph will represent \( y=\sqrt{x}+4 \).

Answer:

Move the blue point to \((0, 4)\), the red point at \(x = 1\) to \((1, 5)\), and the red point at \(x = 4\) to \((4, 6)\) to complete the graph of \(y=\sqrt{x}+4\).