1. Characteristics of Functions

2. Types of Functions Continuous has NO breaks
Discrete has gaps or breaks

3. Domain & Range
The domain of a relation is the set of all inputs or x-coordinates.
The range of a relation is the set of all outputs or y-coordinates.

4. Notation
Set Notation
If the graph is discrete, list all of the inputs or outputs inside the squiggly brackets.
Example: D= {1,2,4,5,7}

5. Notation
Interval Notation For each continuous section of the graph, write the starting and ending point separated by a comma. Parenthesis: point is not included in Domain/ Range Brackets: point is included in Domain/ Range
Start End

6. Notation Algebraic Notation
Use equality and inequality symbols and variables to describe the domain and range.
Examples:
y > 5

7. Intercepts
x-intercept – the point at which the line intersects the x-axis at (x, 0)
y-intercept – the point at which the line intersects the y-axis at (0, y)

8. Find the x and y intercepts, then graph.
-3x + 2y = 12

9. Find the x and y intercepts, then graph.
4x - 5y = 20

10. Increasing, Decreasing, or Constant
Sweep from left to right and notice what happens to the y-values
Finger Test- as you move your finger from left to right is it going up or down?
Increasing goes up (L to R)
Decreasing falls down (L to R)
Constant is a horizontal graph

11. Characteristics
Domain:
Range:
Intercepts:
Increasing or Decreasing?

12. Characteristics
Domain:
Range:
Intercepts:
Increasing or Decreasing?

13. Just for practice, let’s look at an example that is NOT a linear function
Domain:
Range:
Intercepts:

14. Average Rate of Change

15. Rate of Change
A ratio that describes how one quantity changes as another quantity changes
We know it as slope.

16. Rate of Change Positive – increases over time
Negative – decreases over time
Zero- doesn’t change over time
Horizontal movement
Undefined - vertical movement

17. Rate of Change
Linear functions have a constant rate of change, meaning values increase or decrease at the SAME rate over a period of time.

18. Average Rate of Change using function notation

19. Ex 1 Find the Average Rate of Change
f(x) = 2x2 – 3 from [2, 4].

20. Ex 2 Find the Average Rate of Change
f(x) = -4x + 10 from [-1, 3].
m = -4

21. A. Find the rate of change from day 1 to 2.
Ex 3 Find the Average Rate of Change
A. Find the rate of change from day 1 to 2.
m = 11
Days (x)
Amount of Bacteria f(x) 1 19 2 30 3 48 4 76 5
121 6
192
B. Find the rate of change from day 2 to 5.

22. Ex 4 Find the Average Rate of Change Households in Millions f(x)
In 2008, about 66 million U.S. households had both landline phones & cell phones. Find the rate of change from 2008 – 2011.
Year (x)
Households in Millions f(x)
2008 66
2009 61
2010 56
2011 51
m = -5
What does this mean?
It decreased 5 million households per year from 2008 – 11.

23. Characteristics of Functions
Classwork
Characteristics of Functions

24. Characteristics of Functions
Homework
Characteristics of Functions