Question

Which function is represented by the graph?

Answer 1

`y=-√(x+2)-1`

Explanation:

Hi there!

Please take a look at the attached image. This is the parent function of the radical function.

`y=√(x)`

This equation represents the transformations of the parent function:

`y=a√(b(x-h))+k`

a dictates vertical stretch.

b dictates horizontal stretch.

h dictates horizontal translation.

k dictates vertical translation.

If we take a look at the given graph, we can tell that the following transformations have been applied:

- reflection across x-axis (a = -1)

- translation 2 units to the left (h = -2)

- translation 1 unit down (k = -1)

Therefore, the function that represents the graph is:

`y=-√(x+2)-1`

I hope this helps!