Question

The following graph shows the preimage, P(x)=x−−√, and the image after a vertical dilation of I(x)=k⋅P(x).

What is the value of k in this transformation?

Answer 1

k = 3

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

3 √3

4 2

P(x) appears to be the function √x.

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

x f(x)

0 0

1 3

2 3√2

3 3√3

4 6

You can divide the function values of l(x) by P(x).

3/1 = 3

6/2 = 3

The scale factor for the dilation is 3. k= 3.