Relations, Functions and Graphs 1

Section 1Relations and functions

A relation is any rule or pairing that connects inputs with outputs. A function is a special relation where each input has exactly one output. Easy to mix up - two different inputs may share the same output, but one input cannot have two different outputs.

Section 2Domain and range

The domain is the set of input values. The range is the set of output values actually produced. In plain words, domain is what you are allowed to put in, and range is what comes out.

Section 3Function notation

Function notation writes rules like f(x) = 2x + 3. It is read as 'f of x', not f times x. To find f(4), replace x with 4: f(4) = 2(4) + 3 = 11.

Section 4Representing functions

Functions can be shown using words, tables, mappings, ordered pairs, equations, or graphs. The representation changes, but the rule stays the same. A table is useful because it shows exact input-output pairs clearly.

Section 5Testing for a function

A relation is a function if every input appears with only one output. With ordered pairs, check whether an x-value repeats with a different y-value. With a graph, a vertical line should not hit the graph more than once.

Section 6Inverse functions

An inverse function reverses the original function. If f sends 2 to 7, then the inverse sends 7 back to 2. To find an inverse algebraically, write y = f(x), swap x and y, then make y the subject.

Section 7Graph interpretation

A graph can show starting value, rate of change, maximum, minimum, and trends. In a Jamaica phone-credit graph, the y-intercept may show starting credit, while a negative gradient may show credit being used up. The thing to remember is that graph features should be explained in the context of the question.