Chapter 1Chapter 1Section 1.1 Functions

FunctionsFunctionsA Notation of Dependence

◦What does that mean?

Rule which takes certain values as inputs and assigns them exactly one output. ◦The out put is a function of the input

Examples???

FunctionsFunctionsExample:

◦The number of gallons of paint needed to paint a house depends on the size of the house. A gallon of paint covers 250 sq ft.

◦The number of gallons needed, N, is a function of the area to be painted, A. For example, If A = 5000 sq ft, then N = 5000/250 = 20 gallons of paint

N = A / 250What is assigned the input and

output of this problem?

FunctionsFunctionsNotation

◦Writing functions in function notation will allow you to stay consistent and organize the information.

Q = f(t)◦Q = output (dependent variable)◦t = input (independent variable)

FuntionsFuntions Q = Q = ff(t)(t)Knowing what we know about painting

a house and function notation what does the following expression tell us?◦f(10,000) = 40

It takes 40 gallons of paint to paint 10,000 sq ft◦Which is the input, and which is the output?

FunctionsFunctionsHow do you tell if a table is a

function?◦For every input value (x), there is one output value

How can you tell if a graph is a function?◦Vertical Line Test

FunctionsFunctionsThe table to the

right represents a function◦ Why?

Could you make a table that is not a function?

X Y1 84 106 -27 11

FunctionsFunctionsThis table does

not represent a function◦ Why?

Could you make a table that is a function?

X Y4 84 106 -27 11

FunctionsFunctionsThis table does

not represent a function◦ Why?

X Y1 36 3

-10 35 3

FunctionsFunctionsVertical Line Test

◦Draw a Vertical Line on a graph and if the vertical line must cross the desired function once for it to be a function.

◦If the vertical line crosses the desired function more than once, the graph is not a function