Which of the following functions is graphed below

Option: C is the correct answer.

            C.   y=|x+4|-2

We know that the vertex of a absolute value function or a modulus function f(x) of the type:

        f(x)=a|x-h|+k

is denoted by V such that:

          V=(h,k)

By looking at the graph of the function we see that the vertex of the function is:

                        (-4,-2)

A)

               y=|x+4|+2

The vertex of this function is:

              (-4,2)

Hence, option: A is incorrect.

B)

               y=|x-4|+2

The vertex of this function is: (4,-2).

Hence, option: B is incorrect.

D)

                 y=|x-4|-2

The vertex of this modulus function is: (4,-2)

Hence, option: D is incorrect.

C)

                y=|x+4|-2

The vertex of this function is: (-4,-2)

Also, we see that the graph of this function matches the given graph.

           Hence, option: C is correct.

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step-by-step explanation: