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 [math]x[/math]) and then depending on what that input is, it returns an output (say y) by some predefined rule (say [math]f[/math]). The graph of a function f is the set of all points (inputs, outputs) = [math](x,y)[/math] in the plane which satisfy the equation [math]y=f(x)[/math]. You can move the input below and see how the graph give a visual relationship between inputs and outputs for the rule [math]f[/math].
Use the slider on the left to change the function used in the example.
