Question

Which graph is the graph of this fucntion

Answer 1

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 $[0,5]$. The first function comes from the pattern of the square root function $f(x)=\sqrt{x}$ and the second one is a linear function.

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

Moreover, we can prove that:

The graph of $3\sqrt{x+1}$ passes through points (0,3) and (3,6):

$y= 3\sqrt{x+1} \\ \\ \\ \bullet \ (0,3): \\ \\ let \ x=0: \\ \\ y= 3\sqrt{0+1} \therefore y=3\sqrt{1} \therefore y=3(1) \therefore y=3 \\ \\ \\ \bullet \ (3,6): \\ \\ let \ x=3: \\ \\ y= 3\sqrt{3+1} \therefore y=3\sqrt{4} \therefore y=3(2) \therefore y=6$

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.

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