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?

k = 3

Step-by-step 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.