Question

which function is represented by the graph?

Answer 1

Answer:

$y=-\sqrt{x+2}-1$

Step-by-step explanation:

Hi there!

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

$y=\sqrt{x}$

This equation represents the transformations of the parent function:

$y=a\sqrt{b(x-h)}+k$

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:

$y=-\sqrt{x+2}-1$

I hope this helps!