Question

How does the graph of y = sqrt x +2 compare to the graph of the parent square root function?

Answer 1

It is a vertical shift up 2

All transformations of parent functions can be written in the form of y = a*f(x-h) + k

a is the vertical stretch factor as well as vertical reflection

h is the horizontal translation distance

k is the vertical translation distance

Answer 2

Option C is correct

the graph is vertical shift of the parent function 2 units up.

Explanation:

Vertical shift:

To translate the parent function
`f(x)= √(x)` vertically, you can use the function:

`g(x)= √(x)+k`.

When k > 0, the graph translated to k units up

When k < 0, the graph translated to k units down.

As per the statement:

Let the parent function be:

`y = √(x)`

then;

the graph
`y = √(x)+2`

By definition of vertical shift:

k = 2 > 0

Therefore, the graph
`y = √(x)+2` is vertical shift of the parent function 2 units up.