Which function is represented by the graph?

Step-by-step explanation:

An absolute value function has the standard form

where h and k are the coordinates of the vertex (the pointy part of the graph) and the absolute value of a indicates whether or not the graph is the same width as the parent graph or if it is steeper or flatter. If the absolute value of a is greater than 1, the graph is steeper; if the absolute value of a is greater than 0 but less than 1 (in other words a fraction less than 1), the graph is flatter than the parent. If the graph is upside down, there will be a negative out in front of the absolute value of a. Because our graph is in fact upside down, we will choose one of the options that has a negative in front of it. The fact that it has moved UP from the origin, but not side to side, means that the k value is a +1.

If you are familiar with an absolute value parent graph, the lines go through each diagonal of the grid perfectly. It appears that our graph is steeper (or slimmer) than that. That means that not only is our graph upside down, it also has an a value greater than 1. Putting those 2 facts to use along with our k value of +1, makes our obvious choice the first one listed.

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!