1. Functions
TEXTBOOK REFERENCE:
4-6

2. What is a relation? All ordered pairs are relations!
A relation is any set of ordered pairs.
{(3,4), (4,5), (5,6)}
{(3,4), (3,5), (3,6)}
Each number in the set of ordered pairs is called an element.
All ordered pairs
are relations!

3. All x coordinates are different numbers = function!
What is a function?
A function is a relation in which only one x matches with a y
Relation and Function
{(3,4), (4,5), (5,6)}
Relation only
{(3,4), (3,5), (4,6)}
All x coordinates are different numbers = function!

4. Functions as Ordered Pairs
{(4,5), (-1, 0), (3,0)}
All x are different, y does not matter!

5. Functions as Tables
{(4,5), (-1, 0), (3,0)} x y -1 3 4 5

6. Functions as Graphs
A graph that is a function must pass the vertical line test
Which of the graphs below represents a function?
Place your pencil vertically on the graph! If your pencil touches the picture only once, you have a function!
Function

7. Function Parts
A function is a relationship where on thing depends upon another.
A function has three parts:
Input – x (plug in number)
Function Rule– problem (arithmetic or geometric sequence)
Output – y (answer)

8. Making Function Tables
A function table organizes your work
so you can find out what the ordered
pairs are.
Input x
Function
Rule 5x
Output y
Ordered Pairs*
(x, y) 1
5 x 1 5
(1, 5) 2
5 x 2 10
(2, 10) 3
5 x 3 15
(3, 15) 4
5 x 4 20
(4, 20)

9. Making Function Graphs
A function graphs plots the ordered pairs you
found on the coordinate plane
Input x
Function
Rule 2x
Output y
Ordered Pairs*
(x, y) 1
2 x 1 2
(1, 2)
2 x 2 4
(2, 4) 3
2 x 3 6
(3, 6)
2 x 4 8
(4, 8)

10. Real World Function Graphs
Chuck earns $4 an hour cleaning his room. Create
table and graph to represent this situation.
Input X
hours
Function
Rule 4x
$4 x hours
Output Y
Pay $
Ordered Pairs*
(x, y) 1
4 x 1 hour $4
(1, 4) 2
4 x 2 hours $8
(2, 8) 3
4 x 3 hours
$12
(3, 12) 4
4 x 4 hours
$16
(4, 16)

11. What are Linear Equations?
A linear equation is an
equation that forms a
a straight line when
graphed.
y = 2x + 1
y is output although listed first.
X = the input.

12. Steps for Graphing Linear Equations
Create a four-column function table.
Select any four values or numbers to substitute for the input x (I suggest -1, 0, 1, 2)
Perform rule.
Write output.
List ordered pairs.
Graph on Coordinate Plane.

13. Steps for Graphing Linear Equations, cont’d.x
2x+1 y
(x, y) 2
2(2)+1 5
(2, 5) 1
2(1)+1 3
(1, 3)
2(0)+1
(0, 1) -1
2(-1)+1
(-1, -1)

14. Steps for Graphing Linear Equations, cont’d.
Every point on the line is a solution to y =2x +1.