© 2014 Shmoop University, Inc. All rights reserved.
Functions, Graphs, and Limits

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.

Sample Problem

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.

Sample Problem

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).

Sample Problem

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.

Advertisement
Advertisement
Advertisement