Chapter 1 Section 1.1Functions

Functions A 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???

Functions Example: ◦ 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 / 250 What is assigned the input and output of this problem?

Functions Notation ◦ 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)

FuntionsQ = f(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?

Functions How 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

Functions The table to the right represents a function ◦ Why? Could you make a table that is not a function? XY

Functions This table does not represent a function ◦ Why? Could you make a table that is a function? XY

Functions This table does not represent a function ◦ Why? XY

Functions Vertical 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