Functions, Graphs, and Limits
Functions Are Your Friend
Functions are machines. Plug the independent variable into the machine and it spits out the dependent variable.
If y = f(x) = x + 1, then as x gets larger (moves right), y gets larger also (moves up). As x gets smaller (moves left), y gets smaller also (moves down).
Here's something to play with: see what happens to y as we make x larger or smaller.
If y = f(x) = 1 - x, then as x gets larger (moves right), y gets smaller (moves down). As x gets smaller (moves right), y gets larger (moves up).
Say y = f(x) = x2. We start x at -5. As x moves right, y gets smaller until x reaches 0. If, starting at 0, we keep moving x to the right, y starts getting bigger again.
With this function, in order to say whether y is increasing or decreasing as we play with x, we need to know two things: whether x is to the left or the right of zero, and whether x is being moved to the right or left.