domain and range

Question

find the domain and the range of the function

h(x) = √x +6 

Answer 1

Hi Dalia;

h(x) = √x +6

 

I am assuming that both the x and 6 are being square-rooted.

 

The first issue we must acknowledge is that there is no such thing as a negative number which can be square-rooted.  The smallest number which can be square-rooted is zero; 0x0=0.

 

x+6=0

x=-6

 

This means that on the x-axis of the graph, the line begins at -6 and proceeds positively.

 

Henceforth, the domain (i.e., x-values of the line) are

(-6, infinity).

 

The lowest value of h(x) is zero.

h(x) is the y-axis.

The line begins on the y-axis at its zero-point.

Henceforth, the range is

0, infinity.

 

The line begins on the x- and y-axis point of

-6,0

and proceeds positively (i.e., to the right) to infinity.