Chapter 1 – Introducing Functions Section 1.1 – Defining Functions Definition of a Function Formulas, Tables and Graphs Function Notation Section 1.2 – Using Functions to Model the Real World Abstract and Model Domain and Range Discrete and Continuous One Output for Each Input
Chapter 1 – Introducing Functions. Section 1.1 – Defining Functions Definition of a Function Formulas, Tables and Graphs Function Notation Section 1.2 – Using Functions to Model the Real World Abstract and Model Domain and Range Discrete and Continuous One Output for Each Input. - PowerPoint PPT Presentation
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Chapter 1 – Introducing Functions
Section 1.1 – Defining Functions
Definition of a FunctionFormulas, Tables and GraphsFunction Notation
Section 1.2 – Using Functions to Model the Real World
Abstract and ModelDomain and RangeDiscrete and ContinuousOne Output for Each Input
Exercises from Sections 1.1 and 1.2
1/10 – domain of men’s shoe function
5/10 – domain
6/10 - domain
2/13 – function notation
3/13 – function notation
4/13 – function notation
5/13 – function notation
6/13 – function notation
11/32 – function notation
12/32 – function notation
23/33 – weird function
Section 1.3Watching Functions Values Change
pages 17 - 29
Section 1.3 – Watching Function Values ChangeExample 1: women’s shoe size function
w(x) = 3x – 21 y = 3x - 21
y (shoe size) depends on x (foot measurement)HOW?
foot length increases from 9 inches to 9 1/6 inches (by 1/6)
foot length increases from 9 1/6 to 9 1/3 inches (by 1/6)
foot length increase from 10 inches to 10 ½ inches (by 1/2)
foot length increases by a full inch during the course of a career.
What is the change in shoe size when:
x(inches)
9 9 1/6 9 1/3 10 10 1/2
y=3x-21(shoe size)
6 6.5 7 9 10.5
foot length increases from 9 inches to 9 1/6 inches (by 1/6)
foot length increases from 9 1/6 to 9 1/3 inches (by 1/6)
foot length increase from 10 inches to 10 ½ inches (by 1/2)
foot length increases by a full inch during the course of her career.
shoe size increases by 0.5
shoe size increases by 0.5
shoe size increases by 1.5
shoe size increases by 3
Example 1
Do you see a pattern?
Change in x(inches)
1/6 1/6 1/2 1
Change in y(shoe size)
0.5 0.5 1.5 3
change in y is always 3 times the change in x
or
change of one unit in x always produces a change of 3 units in y