Vertical line testing For each input in the declared domain, its vertical line must meet the graph exactly once. Across the whole graph, no vertical line may meet it more than once. To reject a function claim, identify an allowed input with no output or more than one output. Function: each vertical line cuts at most once. Function: each vertical line cuts at most once. Non-function: the displayed vertical line cuts more than once. Non-function: the displayed vertical line cuts more than once. Horizontal line testing A function is one-one if every horizontal line cuts its graph at at most one point. To show it is not one-one, give a specific horizontal line y=k that cuts the graph twice or more. One-one function One-one function Not one-one Not one-one

For each input in the declared domain, its vertical line must meet the graph exactly once. Across the whole graph, no vertical line may meet it more than once. To reject a function claim, identify an allowed input with no output or more than one output.

A function is one-one if every horizontal line cuts its graph at at most one point. To show it is not one-one, give a specific horizontal line \(y=k\) that cuts the graph twice or more.

Functions

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Functions and one-to-one tests

Functions and one-to-one tests