Question

Which of the following graphs shows the preimage P(x)=2√x and the image I(x)=−P(x)?

Answer 1

The graph showing red and blue making a U is the correct choice.

Explanation:

The graph P(x) is a square root function. It has a vertex of (0,0) and has the following points:

x f(x)

0 0

1 1

2 2√2

3 2√3

4 4

The image of l(x) = -P(x) changes the points of the function to

x f(x)

0 0

1 - 1

2 - 2√2

3 -2√3

4 -4

This makes the graph reflect across the x-axis. The graph with the U shape made by both functions together is the correct choice.