1. Foundation of Functions Relations and Functions/ Domain and Range
Unit 1
Foundation of Functions
Relations and Functions/
Domain and Range

2. Relations and Functions
Functions vs. Relations
A "relation" is just a relationship between sets of information. Any (x,y), can be a relation. Just a point on a graph can be a relation.
A “function” is a well-behaved relation, that is, for any x (input), there is only one y (output).

3. Relations and Functions
Functions vs. Relations
All “functions” are relations!!!
But not all relations are “functions”

4. Relations and Functions
What is a function?
“a function is…a relation in which every input is paired with exactly one output”

5. Relations and Functions
Relations can be written in several ways:
ordered pairs,
table,
graph, or
Mapping
Situation

6. Relations and Functions
Order Pair Table
{(3, 4), (7, 2), (0, -1),
(-2, 2), (-5, 0), (3, 3)}

7. Relations and Functions

8. Relations and Functions
Which mapping represents a function?

9. Relations and Functions
Which mapping represents a function?
Choice One Choice Two 3 1 –1 2 2 –1 3 –2

10. Domain: The set of all x-values That will work RANGE:
Domain and Range
Domain:
The set of all x-values
That will work
RANGE:
The set of all y-values

11. Notations Set Builder Notation Inequality Notation Interval Notation
Domain and Range
Notations
Set Builder Notation
Inequality Notation
Interval Notation

12. Domain and Range
Set Builder Notation
Domain:
Range:

13. Domain and Range
Inequality Notation
Domain:
Range:

14. Set Builder and Inequality
Domain and Range
Set Builder and Inequality
Set Builder Notation
Inequality Notation
Set Builder Notation and Inequality Notation are almost the same. You can use either one.

15. Domain Range Domain and Range Interval Notation
[ means less than or equal
] means greater than or equal
( means less than <
) means greater than >

16. Set Builder, Inequality and Interval Notations
Domain and Range
Set Builder, Inequality and Interval Notations

17. You can find domain & range given in a variety of modes:
Domain and Range
You can find domain & range given in a variety of modes:
Table
Set of points
Mapping
Equation
Graph
Situation

18. Table Domain and Range Domain: ____________ Range: _____________ NO
{ x: 2, 3, 4 } x y 4 3 2 5 7 9
{ y:3, 5, 7, 9}
Function? _____ NO
Why, because for the x=4 there are two different values for y. For every input there can only be one output

19. Set of Points Domain: Range: Domain and Range
{(1,0), (-1,1), (1,2), (-3,3)}
Domain:
Range:
{x:-3, -1, 1}
{y:0, 1, 2, 3}
Function? _____ No
Why, because for input, x there is more than one output for y

20. Mapping 7 2 9 3 4 6 -1 Function? _____
x y
Domain:
Range:
{x:-1, 2, 4, 7}
{y:3, 6, 9}
YES
Function? _____
Why, because for every x input there is only one y output.

21. Find the range of the given equation when the domain is {x: -5, 0, 5}:
{y:-1, 74}
How, substitute each of the x values in the equation and work it out:
OR, put the equation in your calculator and go to second table and find the y values

22. Equation y = 5x - 1 Domain: x < 3 Range: y<14
How, substitute x=3 in the equation: y=5(3)-1=14
OR, put y=5x-1 in your calculator, go to 2nd Table and see what the y values are.

23. Situation
Maria earns $7 per hour for baby-sitting after school and on Saturday. She works no more than 16 hours a week.
Independent:
Time
Dependent:
Amount of Money
Domain:
Range:

24. Graph D: R:
{X:-3, -2, 0, 2}
(0, 4)
{y:-1, 0, 3, 4}
(-2, 3)
This is a DISCRETE Graph since the points are not connected
(-3, 0)
(2, -1)

25. Graph D: R: 4
This graph is a CONTINUOUS graph since the points are connected.
- 6 5
- 4

26. LET’S PRACTICE!

27. Table Domain: ___________ Range: ____________ x y 4 5 15 3 -1 1010
Domain: ___________
Range: ____________
{x: -1, 0, 3, 4, 5 }
{ y: 0, 5, 10, 15}

28. Set of Points Domain: Range: {(2, 3), (5, 2), (-1, 3)} {x: -1, 2, 5}
{y: 2, 3}

29. Mapping 3 5 1 10
x y
Domain:
Range:
{x: 1, 3, 5}
{y: 0, 5, 10}

30. Find the range of the given equation when the domain is {x: -2, 0, 4}:
y = 2x – 4
Range:
{y:-8, -4, 4}

31. Find the range of the given equation when the domain x ≥ 5:
y = 7x + 2
Range:

32. Graph D: R:
{X:-6, -2, -1, 3, 5}
{Y:-6, -4, -1, 5}
Is the graph is Continuous or Discrete
Discrete

33. Graph D: 5 R:
- 4 2
- 4
Graph is Continuous

34. Graph D: 1
- 1 6 R:
- 6
CONTINUOUS Graph

35. Graph D: R: Continuous Graph ∞ 3 - ∞ - 5 No top y-boundary
No left x-boundary
- ∞
- 5
Continuous Graph

36. Situation
Tara’s car travels about 25 miles on one gallon of gas. She has between 0 and 12 gallons of gas in the tank.
Independent:
Dependent:
The number of gallons of gas
Distance travel
Domain:
Range:
0 to 12 gallons of gas
0 to 300 miles