2015 the institute for the professional development of adult educators what is a function?
TRANSCRIPT
2015 The Institute for the Professional Development of Adult Educators
What Is a Function?
2015 The Institute for the Professional Development of Adult Educators
What is a function?
2
Functions
2015 The Institute for the Professional Development of Adult Educators
A function is a relation in which each element of the domain is paired with exactly one element of the range. Another way of saying it is that there is one and only one output (y) with each input (x).
f(x)x y
Functions
3
2015 The Institute for the Professional Development of Adult Educators
Function Notation
Output
InputName of Function
y f x
Functions
4
2015 The Institute for the Professional Development of Adult Educators
Functions
5
In order for a relationship to be a function . . .
INPUT
(DOMAIN)
OUTPUT (RANGE)
FUNCTIONMACHINE
EVERY INPUT MUST HAVE AN OUTPUT
TWO DIFFERENT INPUTS CAN HAVE THE SAME OUTPUT
ONE INPUT CAN HAVE ONLY ONE OUTPUT
2015 The Institute for the Professional Development of Adult Educators
Which of the following relations are functions?
6
R= {(9,10), (-5, -2), (2, -1), (3, -9)}
S= {(6, a), (8, f), (6, b), (-2, p)}
T= {(z, 7), (y, -5), (r, 7) (z, 0), (k, 0)}
No two ordered pairs can have the same first coordinate
(and different second coordinates).
R is a function.
Is It a Function?
2015 The Institute for the Professional Development of Adult Educators7
Input Output
-3 3
1 1
3 -2
4
Domain (input) = {-3, 1,3,4}Range (output) = {3,1,-2}
Function?Yes: each input is mappedonto exactly one output
Is It a Function?
2015 The Institute for the Professional Development of Adult Educators8
1. {(2,5) , (3,8) , (4,6) , (7, 20)}
2. {(1,4) , (1,5) , (2,3) , (9, 28)}
3. {(1,0) , (4,0) , (9,0) , (21, 0)}
Is It a Function?
2015 The Institute for the Professional Development of Adult Educators
Vertical Line Test: a relation is a function if a vertical line drawn through its graph, passes through only one point.
Is It a Function?
9
AKA: “The Pencil Test”
Take a pencil and move it from left to right (–x to x); if it crosses more than one point, it is not a function.
2015 The Institute for the Professional Development of Adult Educators
Vertical Line Test
Would this graph be a function?
NO
Is It a Function?
10
2015 The Institute for the Professional Development of Adult Educators
This is a function because no vertical line can be drawn so that it intersects the graph more than once.
A function is a relation in which each element of the domain is paired with exactly one element of the range. When x = 0, y = 1 and y = 6. So, this relation is not a function.
Which are functions and why?
This is a function because no vertical line can be drawn so that it intersects the graph more than once.
Is It a Function?
11
2015 The Institute for the Professional Development of Adult Educators
Quick Review
Which relations below are functions?
a. Names and social security numbers
b. Addresses and names
c. {(2,4) (-2, 5) (3, 7)}
d. {(4 ,1) (4, 3) (5, 6)}
e. { (2,5) (3, 5) (4,5)}
12
2015 The Institute for the Professional Development of Adult Educators13
Real World Examples of Functions• Distance (output) and time (input) during a trip
– For example, if you are traveling, the distance that you travel depends on the time that you spend on the road.
• Amount of money earned (output) and hours worked (input)– For example, if you work in a fast food outlet, your
pay packet depends on the number of hours you work. Or, the amount of concrete you need to order when constructing a building will depend on the height of the building.
Connection
2015 The Institute for the Professional Development of Adult Educators©2014 IPDAE. All rights reserved. All content in this presentation is the proprietary property of The Institute for the Professional Development of Adult Educators14
2015 The Institute for the Professional Development of Adult Educators
www.floridaipdae.org15