1. Unit 1.1 Dependency Relationships

2. Definitions…
Relation – a set of ordered pairs that represent a mapping/pairing of input values with output values
Function – a special type of relation in which each x value is paired with exactly one y value
Domain – the set of all x values in a relation
Range – the set of all y values in a relation
Independent Variable: The input variable (in most cases x).
Dependent Variable: The output variable (in most cases y).

3. Identifying Functions
If any of the x values repeat then the relation is NOT a function.
Is it a function? X -2 4 6 5 7 y -3 1
It is a function!

4. Mapping Relations
Process of matching the elements of the domain with the elements of the range.
Remember that in order to be a function only one member of the domain can map to one member of the range.

5. Independent & Dependent
What is independent?
What is dependent?
State the independent and dependent:
H = 3P
Where are they usually in a table?
Where are they usually on a graph?

6. Inequality Form: Domain and Range
*If the graph touches it or has a solid circle, you use a ≤ (less than or equal to) *If the graph approaches and never touches (has an open circle or approaches infinity) use a < (less than) Domain: Range:
Lowest X-value
Inequality X
Highest
X-value
Lowest
Y-value
Inequality Y
Highest

7. Interval Notation
Hard Brackets [ ]are like less/more than or equal to [ ]
Soft Brackets are like less than or more than ( )

8. Graphs inequality and interval notation
Domain: Domain:
Range: Range:
-7 ≤ x ≤ 0 or [-7,0]
-6 < x < 4 or (-6, 4)
-6 < y ≤ 4 or (-6, 4]
0 < y ≤ 7 or (0, 7]

9. {-4, -1, 5} Domain: Domain: Range: Range: {-2, 3, 6, 8}
All Real Numbers
{-2, 3, 6, 8}
-4 ≤ y < ∞ or [-4,+ ∞)

10. Domain: Domain: Range: Range: All Real Numbers All Real Numbers

11. Relations Relation: ( 0, 32) ( 0, 16) (1, 8) ( -3, 4) ( 2, 7) Domain:
Range:
( -4, 5) ( 0, -3) (1,0) ( 3, 5) ( 5, 9)
Domain: ______________
Range: _______________
{0, 1, -3, 2}
{32, 16, 8, 4, 7}
{-4, 0, 1, 3, 5}
{5, -3, 0, 9}

12. Mappings -4 -2 3 7 4 6 -5 1 3 5 7 6 2 4 Domain: Domain: Range: Range:
{1, 3, 5, 7}
{-4, -2, 3, 7}
{6, 2, 4}
{4, 3, 6, -5}
NOTE: You don’t need to write the 6 twice

13. Tables of Values x y -2 2 1 3 4 x y 1 2 4 3 9 x y -2 2 4 16 {-2, 0, 3}1 3 4 x y 1 2 4 3 9 x y -2 2 4 16
{-2, 0, 3}
{0, 1, 2, 3}
{-2, 0, 2, 4}
Domain: __________ Domain: _________ Domain: _________
Range: ___________ Range: ___________ Range: __________
{2, -2, 1, 4}
{0, 1, 4, 9}
{0, 4, 16}

14. Definitions
A discrete function means the graph is a set of data (points) – it has a countable number of points in it
A continuous function means the graph has no breaks in it – you can draw the graph without picking up your pencil.

15. Examples
Discrete
Continuous

16. Discrete or Continuous?
The CHS cheerleaders are selling candy bars for $1.50 each. The function f(x) gives the amount of money collected after selling x candy bars.
The function is discrete, because you cannot sell part of a candy bar.

17. Discrete or Continuous?
A hose releases water at a rate of 2 gallons per minute. The function f(x) gives the amount of water released after x minutes.
The function is continuous, because you can have part of a minute.

18. Practice Time Amount of money the gym makes Total points earned
Number of Games
Total points earned
Number of people buying memberships
Depth
Type of car sold
Cost of stamp
Altitude
Pressure
Time
How much money he earns
Distance on the ground

20. Problem Situation #1 Is it a function? YES!! Independent Variable
Domain:
Range:
YES!!
# of hours
Paycheck amount
0 ≤ x < ∞ or [0, + ∞)
0 ≤ y < ∞ or [0, + ∞)

21. Problem Situation #2 Is it a function? YES!! Independent Variable
Domain:
Range:
YES!!
# of jars
Money raised
Integers greater than 0
Integer multiples of 10 greater than 0