graph the square root function of h(x) = -√x-1; State the domain and range

Question

Graph the square root function of h(x) = -√x-1; State the domain and range.

Answer 1

Hi,

First, determine the domain and range of the parent function, f(x) = √x.

1. Domain = (0, ∞ )
2. Range =( 0 , ∞ )

Second, identify the transformation of the function h(x) = -√x -1 , from the parent function.

• Reflected across the x-axis and shift down 1 unit. Domain =(0, ∞ ) and Range =( -1, - ∞ )

However, if the function h(x) = -√(x -1) , the transformation from the parent function will be 

• Reflected across the x-axis and shift right 1 unit. Domain =(1, ∞ ) and Range =(0, - ∞ )

 

In order to graph, you may use the transformation or make a table of values and connect the dots to make the curve.

 

I think this is helpful.

 

SN