The domain of a function represents the input values. Here the domain stands for the x-values. Since the square root of a negative does not exist in the real number system, 2x+4 must be greater than or equal to 0. So the domain is found by solving the inequality:
The allowable x-values must be greater than or equal to -2.
The range represents the output of the function. Here the range stands for the y-values. Since x=-2 is the smallest value of x, the smallest value for y is found by:
y=1/2 sqrt (2(-2)+4) - 3
y=1/2 sqrt (0) - 3
The range of the function is `y>=-3`
Here is a graph that shows the graph exists for x's greater than or equal to -2 and y's greater than or equal to -3.