Step-by-step explanation:
Hi!
So, this is peicewise function. That means that x values have to be in a certain range in order to have a function. Look at this piecewise function, for example:
When x is 2, you use the equation 7x+2.
When x is 13, you use the equation x=2.
Now we can use this graph to figure out the definition by looking at the points. An open circle means that a point can't reach that point (less than or greater than). A closed circle means that a point <em>can </em> touch there( less than or equal to and greater than or equal to).
So here, we have a closed circle at (-1, 1) and an open circle at (-1,2).
So, for all points that are less than or equal to -1, there will be a specific equation.
For all points greater than -1, there will be a different equation.
{this is based on x-values, btw}
So let's use these points to figure out the equations.
Check 2x + 2.
2(-1) + 2
-2 + 2 =0
This doesn't work.
Check 2x + 4
2 (-1) +4
-2 + 4 =2
This doesn't work.
Check x-2
-1-2 = -3
This doesn't work.
Check x + 2
-1 + 2 = 1
This works. Therefore, we can say that D is the answer.