Which equation represents the function graphed on the coordinate plane?

a. g(x) = |x – 4| – 10.
b. g(x) = |x + 4| – 10.
c. g(x) = |x – 10| + 4.
d. g(x) = |x + 10| – 4.

The two lines connect at (-4,-10)This means you would add 4 to x and then subtract 10 from the equation.

This means the answer is: B.g(x) = |x + 4| – 10.

Step-by-step explanation:

The second option shows the function represented in the given graph.

Basically, the graph shows an absolute value function, because it has the form of a "V".

We know that the parent function of this is , which is the simplest form of a value absolute function. So, we can get the right answer by just applying all given transformations to the parent function.

In the graph we see that the function was move 10 units downside, and 4 units to the left. This means that the function has to have "-10" and "+4", where the negative indicates the downside movement, and the positive sign indicates the left-side movement.

It's important to remember that, in case of horizontal displacement, with add to move to the left, and we subtract to move to the right.

Applying these translation to the parent function, we have

Therefore, the right answer is option B.