A "function" is a black box, with a funnel on top, a little door on the bottom, and a crank on the side. The way it works is:
-- You take a number, and call it 'x'.
-- You drop it into the funnel on top of the box, and you turn the crank.
-- Some gears, shafts, math operations and stuff inside the box do things to 'x', and eventually the little door on the bottom opens up and another number falls out.
-- Before you even touch that one, you call it 'y', and then you pick it up and look at it.
The number that falls out is related somehow to 'x'. It depends on 'x', AND on exactly what's inside the box ... how the gears and shafts and math operations are all hooked together. All the guts and parts inside DETERMINE what the box will do to 'x', and how 'x' will get changed, and what will come out the bottom.
We call 'y' the FUNCTION of 'x'.
If you know exactly what's inside the box, then even before you drop 'x' into the funnel, you can always tell in advance WHAT will come out.
If you DON'T know what's inside, then the only way you can describe the function is to take a bunch of numbers, drop them into the function one at a time, LOOK and SEE what comes out each time, and write it all down.
THAT's what this question is giving you.
What comes out is called the VALUE of the function for each 'x' that you drop in. The table is giving you the VALUE of 'y' (the function) for seven different 'x's. Then the question just wants you to look and see what falls out of the box when 'x' is -1 .
Look at the table. It says that when 'x' is -1, 'y' is going to be <em>3 </em>. That's the answer to the question.
We still don't know anything about what's inside the box. We don't know the structure of the FUNCTION, and exactly what it does to 'x' to produce 'y'. But we do know what'll fall out if we drop a -1 into the funnel ... because the table tells us !
Now, please get up off your knees. It's unbecoming.
