2nd Hour Honors Pre-Calculus Winter 2013: Functions and Their Graphs: 1.1

A function is relationship involving one or more variables. Functions have an input and output. The input is the first coordinate of the ordered pair and the output is the second coordinate. In the example below, the input values are a, b, c, and d, and the output values are p, q, and r.

Note the following characteristics of the function above that will apply to other functions:

(1) Each element in A is paired with an element of B

(2) Some elements in B may not be paired with any element in A

(3) Two or more elements of A may be matched to the same element of B

Also, if an element of B were to be paired with two elements of A, then the picture would not represent a function.

i.e. a-->p a-->p

b -->q b-->q

b-->r c-->q

c-->p d-->r

NOT A FUNCTION FUNCTION

Functions must pass the vertical line test:

Function Notation is just a way to represent that the equation is a function.

To evaluate a function, you must enter the input value into the output, and then solve. This next example shows the evaluation of g(x)= 3/(10-7x) for the solution of x when we have g(x)=g(2):

A Piecewise-Defined Function is simply a function in Piecewise Form, which may sound confusing, but the main idea is shown below (the lines show the solutions to the function):