Which of the following functions is graphed below

y = | x + 3 | - 4

which agrees with option "D" in the list of possible answers

Step-by-step explanation:

Every time you have an absolute value function, notice that the vertex when the function goes from let's say decreasing to increasing (or viceversa), must be located at the x-value for which the argument of the absolute value (the expression inside the absolute value)  is zero.

Notice in the graph that the x-value where such happens is at x = -3. Such case corresponds to an absolute value of the form: |x + 3|.

Now, realize that this vertex doesn't lie on the x-axis, but 4 units below. That means that the function has been translated vertically down 4 units, Such transformation corresponds to subtracting 4 from the absolute value expression. Therefore, the functional expression for this graph must be:

f(x) = | x + 3 | - 4

which coincides with the last function in the list of possible answers.

answer:

c. the third graph