Question

graph the domain of the function on a number line.
h(x)= square root of 6x+12

Answer 1

The function of square root is not defined on the real plane for negative values. So, our restriction on the domain would be the numbers for which 6x + 12 < 0.
6x + 12 < 0
6x < -12
x < -2

These are the points where h(x) is NOT defined. So, the interval for which our function IS defined (the domain) is everything not in x<-2, or x >= -2.

We would graph this on a number line like...