relations & functions an introduction for algebra students
TRANSCRIPT
Relations & Functions
An Introduction for
Algebra Students
Created by Cathy Stevens 2November 2001
A relation is any set of ordered pairs.
{(x, y), (-5, 6), (4, 7), (6, 8)}
Created by Cathy Stevens 3November 2001
Relations can be written in different ways
As a list of coordinate points…{(3,1), (-4,5), (5,0)}
As a table of values…
As an equation…
y = 3x-1
As a graph…
x 1 2 3 y 2 4 6
Created by Cathy Stevens 4November 2001
The domain of a relation is all the first coordinates of the ordered pairs.
{(0, -2), (3, 1), (3, 5), (8,-4)}
Domain: {0, 3, 8}
Created by Cathy Stevens 5November 2001
The range is all the second coordinates in a relation.
{(0, -2), (3, 1), (3, 5), (7, -9)}
Range: {-2, 1, 5, -9}
Created by Cathy Stevens 6November 2001
Check out this machine!
Input
Output
Created by Cathy Stevens 7November 2001
Think of a relation in terms of input and
output
Input, x
035
-2156
Output, y
Created by Cathy Stevens 8November 2001
The Vocabulary of Relations
XInputDomain
RangeOutputy
Created by Cathy Stevens 9November 2001
A function is a relation in which no two ordered pairs have the same x-value.
{(2, -3), (4, 5), (6, 5), (7,9)}
Created by Cathy Stevens 10November 2001
Examine these relations to see if they are
functions.
{(0, -3), (2, 5), (4, 7), (5, -8)} Function?
{(2, 4), (5, 3), (5, -7)} Function?
Created by Cathy Stevens 11November 2001
Are these relations functions?
{(2, 4), (3, 4), (5, -7)}
{(3, -2), (3, 5), (6, 4)}
x 3 4 4 y 0 -2 -4
Input 3 7 8 Output 0 -4 -4
Created by Cathy Stevens 12November 2001
-1
The Real Function Machine
f(x)= 3x + 5
f(1)= 3(1) + 5
= 3 + 5
= 8
Input
x
Output
f(x)
Created by Cathy Stevens 13November 2001
The Vertical Line Test
A relation is a function in which no vertical line crosses its graph in more than one point.
Created by Cathy Stevens 14November 2001
Use the vertical line test
Function?Function?
Created by Cathy Stevens 15November 2001
Challenge
Write three relations, one in each format.
Ordered PairsA table (T-chart)A graph
Challenge a classmate to determine which relations are functions.