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