1.4 Function

relation

a connection or association between elements of one or more sets

function

a rule that assigns to each x input exactly one y output

domain

set if inputs (x)

range

set of outputs (y)

Four Ways to Represent a Function

Verbally, Numerically, Graphically, and Algebraically

Verbally Function expression

by a sentence that describes how the input variable is related to the output variable

Numerically Function expression

a table or a list of ordered pairs that matches input values with output values

Graphically, function expression

points in a coordinate plane in which the horizontal positions represent the input values and the vertical positions represent the output values

Algebracally, function expression

an equation in two variables

What makes an equation not function

If one x-value gives more than one y-value

piecewise-defined function

A function defined by two or more equations over a specified domain

implied domain

the set of all real numbers for which the expression is defined

Difference Quotient

f(x+h) - f(x)/h , h does not equal 0