Question

Using y= √x as the parent function, make your own transformations (5 units right, reflect on x axis, 2 units down, horizontal compression with factor 2). Then graph and state domain and range.

Answer 1

You have the following parent function:

y = √x

after a transformation of 5 units right you obtain:

√x => √x + 5

a reflection around the x-axis results in:

√x + 5 => -√x - 5

a transformation of 2 units down is given by:

-√x - 5 => -√x - 5 - 2 = -√x - 7

and finally, a horizontal compression with factor 2, results in:

-√x - 7 => -√(2x) - 7

The graph of the previous result is shown below:

as you can notice, the domain and the range are:

domain: (0 , oo)

range: (-7 , -oo)