Question

Which graph is the graph of this fucntion

Answer 1

Graph C

Explanation:

This is a piecewise-defined function because it is defined by two equations over a specified domain and this domain is
`[0,5]`. The first function comes from the pattern of the square root function
`f(x)=√(x)` and the second one is a linear function.

The graph of
`3√(x+1)` has been shifted one unit to the left of
`f(x)=√(x)` and stretched vertically where each y-value is multiplied by 3.

Moreover, we can prove that:

The graph of
`3√(x+1)` passes through points (0,3) and (3,6):

`y= 3√(x+1) \\ \\ \\ \bullet \ (0,3): \\ \\ let \ x=0: \\ \\ y= 3√(0+1) \therefore y=3√(1) \therefore y=3(1) \therefore y=3 \\ \\ \\ \bullet \ (3,6): \\ \\ let \ x=3: \\ \\ y= 3√(3+1) \therefore y=3√(4) \therefore y=3(2) \therefore y=6`

It passes through these points.

The graph of
`5-x` passes through points (5,0) and (3,2):

`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`

It passes through these points.

____________________

Finally, the graph is shown bellow and matches Graph C.