Question

Can someone please help me understand how to solve this? I can't seem to wrap my head around this concept so if someone could possibly explain it to me or refer me to a great resource I'd be very thankful. Thank you!

Answer 1

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:

$\left \{ {{7x+2 } \atop {x=2}} \right.$ ${ {{x=2} \atop {x=13}} \right.$

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 can 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.