Given:
A function:
[tex]g(x)=\sqrt{x+5}[/tex]
To find:
a. The domain of the function.
b. Graph of the function.
c. The range of the function.
Solution:
a.
The domain of a function is the set of all x values for which g(x) exists as a real number.
For the given function, x can only take values greater than -5 because if we take x value less than -5, the value in the root becomes negative and g(x) becomes an imaginary number.
Thus, the domain of the function is :
[tex][-5,\infty)[/tex]
b.
The first graph has the required domain.
Thus, the first graph is correct.
c.
From the graph, it is clear that the curve of the function lies above the y-axis. So, the range of the function is :
[tex][0,\infty)[/tex]
