Answer:
Graph C
Step-by-step explanation:
This is a piecewise-defined function because it is defined by two equations over a specified domain and this domain is [tex][0,5][/tex]. The first function comes from the pattern of the square root function [tex]f(x)=\sqrt{x}[/tex] and the second one is a linear function.
The graph of [tex]3\sqrt{x+1}[/tex] has been shifted one unit to the left of [tex]f(x)=\sqrt{x}[/tex] and stretched vertically where each y-value is multiplied by 3.
Moreover, we can prove that:
The graph of [tex]3\sqrt{x+1}[/tex] passes through points (0,3) and (3,6):
[tex]y= 3\sqrt{x+1} \\ \\ \\ \bullet \ (0,3): \\ \\ let \ x=0: \\ \\ y= 3\sqrt{0+1} \therefore y=3\sqrt{1} \therefore y=3(1) \therefore y=3 \\ \\ \\ \bullet \ (3,6): \\ \\ let \ x=3: \\ \\ y= 3\sqrt{3+1} \therefore y=3\sqrt{4} \therefore y=3(2) \therefore y=6[/tex]
It passes through these points.
The graph of [tex]5-x[/tex] passes through points (5,0) and (3,2):
[tex]y=5-x \\ \\ \\ \bullet \ (5,0): \\ \\ let \ x=5: \\ \\ y=5-0 \therefore y=5 \\ \\ \\ \bullet \ (3,2): \\ \\ let \ x=3: \\ \\ y=5-3 \therefore y=2[/tex]
It passes through these points.
____________________
Finally, the graph is shown bellow and matches Graph C.
