Visualizing Functions as Graphs

In the applet below is intended to help you understand the connection between the graph of a function and the function itself.

Recall that a function can be thought of as a machine which takes an input in (say x) and then depending on what that input is, it returns an output (say y) by some predefined rule (say f). The graph of a function f is the set of all points (inputs, outputs) = (x,y) in the plane which satisfy the equation y=f(x). You can move the input below and see how the graph give a visual relationship between inputs and outputs for the rule f.

Use the slider on the left to change the function used in the example.

Jamie Mulholland
Department of Mathematics
Simon Fraser University
Created with GeoGebra