1. Introduction to Functions
What’s New?
Coordinate Plane, or System
Domain and Range
Not a Function At All!
What is a Function?
Students will need a copy of the Vocabulary Notes
Cain Oct ‘08

2. A function is graphed on a coordinate plane, or system.
Introduction to Functions
Coordinate Plane, or
Coordinate System
A function is graphed on a coordinate plane, or system.
2-Dimensional Graphs
Vertical axis (up and down) is the y-axis called the RISE
Horizontal axis (left and right) is the x-axis called the RUN
Where they intersect is the
origin

3. (3,1) Coordinate Plane or Coordinate System
2-Dimensional Graphs
Ordered Pairs give the placement of a point on a graph
First number is the value on the x-axis
Second value is the value on the y-axis
(3,1) 1 3

4. What is the ordered pair naming the black point?
Coordinate Plane or Coordinate System
Domain and Range
2-Dimensional Graphs
Ordered Pairs give the placement of a point on a graph
What is the ordered pair naming the black point?
(0,0)
Where would (-2,3) be?
2. Where would (-3,0) be?
3. Where would (3,-3) be?
4. Where would (-1,-2) be?

5. Ordered Pairs give the placement of a point on a graph
Domain and Range
2-Dimensional Graphs
Ordered Pairs give the placement of a point on a graph
A set of ordered pairs is a relation
first value x-value is the Domain
second value y-value is the Range
{(-2,3), (-3,0), (3,-3), (-1,-2)}
Domain is {-3, -2, -1, 3}
What is the Range?
What is the Domain?
Range is {-3, -2, 0, 3}

6. Domain and Range {- 2 , 0, 2, 4} {- 3 , - 1, 1, 3} {- 5 , -2, 1, 4}
What is the domain and range of the graph?
{- 2 , 0, 2, 4}
DOMAIN:
RANGE:
{- 3 , - 1, 1, 3}
DOMAIN:
What is the domain and range of the table?
{- 5 , -2, 1, 4} x -5 -2 1 4
f(x) -1
RANGE:
{- 2 , - 1, 0, 1}

7. Introduction to Functions
What is a Function?
A function is a relation in where each member of the domain is paired with exactly one member of the range.
Each x-value is used
once AND ONLY once.
No x-value is repeated with a different value of y. x 1 2 3
f(x) -2 -1 x -5 -2 1 4
f(x) -1
Is this a function?
YES NO

8. Not a Function At All! GRAPHS with points and lines
To check whether a graph is a function, use the vertical line test.
The vertical line test: if you can draw a vertical line anywhere and it touches 2 points or crosses a line twice, it is Not a Function At All!
Are these 4 points a function?
Is this black line a function? NO NO

9. Relations in Tables or Sets This is Not a Function At All!x 1 2 3
f(x) 4
Is each member of the domain paired with exactly one member of the range?
This is Not a Function At All!
{(-2,3), (-3,0), (3,-3), (-2,-2)}
x = 1 is repeated with 2 values of y!
This is Not a Function At All!
x = -2 is repeated with 2 values of y!

10. What is a Function? GRAPHS with points and lines
Using the vertical line test, are these points a function?
YES
Is the black line a function?
YES

11. Relations in Tables or Sets
What is a Function?
Relations in Tables or Sets x 1 2 3 4
f(x) -3 -1 x 1 2 3 4
f(x)
Is each member of the domain paired with exactly one member of the range?
This is a Function!
This is a Function!
WAIT! Each value for the range (y) is 4! Does that matter?
{(-4,3), (-3,2), (-2,1), (-1,0)}
NO! Only the domain matters!
This is a Function!

12. relation: a set of ordered pairs
What is a Function?
REVIEW
A function is a relation in where each member of the domain is paired with exactly one member of the range.
relation: a set of ordered pairs
Each x-value is used
once AND ONLY once.
No x-value is repeated with a different value of y.