Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y=3\sqrt{x+2}[/tex]
Remember that the radicand must be greater than or equal to zero
so
[tex]x+2\geq 0[/tex]
solve for x
subtract 2 both sides
[tex]x\geq -2[/tex]
The domain is the interval [-2,∞)
All real number greater than or equal to -2
For x=-2
[tex]y=3\sqrt{-2+2}=0[/tex]
so
The range is the interval [0,∞)
All real number greater than or equal to 0
Find the y-intercept
Remember that the y-intercept is the value of y when the value of x is equal to zero
For x=0
[tex]y=3\sqrt{0+2}[/tex]
[tex]y=3\sqrt{2}[/tex]
[tex]y=4.243[/tex]
The y-intercept is the point (0,4.243)
therefore
The graph in the attached figure
