1. UPCOMING QUIZ and TEST DATES: Wed 10/1: Quiz - Sections 2.1 - 2.4
Algebra Monday, 9/22/14
Warm-ups: pre-req skills needed for Chapter 2 (pg 57 #1-19 all)
Discussion/Notes/Guided Practice: 2.1 Relations and Functions
HW:  A#2.1 pages #13-22 all; and #24-42 evens -- due Tues
UPCOMING QUIZ and TEST DATES: Wed 10/1: Quiz - Sections

2. WARM-UPS: Complete page 57 #1-19 all write your answers on this page

3. 1. Identify the BIG Ideas for Chapter 2
5. Determine if a graph is discrete or continuous
2. Define key vocabulary terms for Section 2.1
6. Understand and use the vertical line test to determine if a graph is a function
3. Analyze and graph relations
4. Determine if a relation is a function
7. Find functional values
Success Criteria:  Q&A, Guided Practice Problems, HW

4. Preview of Chapter 2 Linear Relations and Functions
Learning target #1
Use your textbook and identify the five “BIG Ideas” for Chapter 2:

5. Preview of Chapter 2 Linear Relations and Functions
Analyze relations and functions
Identify, graph, and write linear equations
Find the slope of a line
Draw scatter plots and find prediction equations
Graph special functions, linear inequalities, and absolute value inequalities

6. Vocabulary for this section – How many do you already know?
Learning target #2
Ordered pair:
One-to-one function:
Cartesian coordinate plane:
Discrete function:
Quandrant:
Continuous function:
Relation:
Vertical line test:
Domain:
Independent variable:
Range:
Dependent variable:
Function:
Function notation:
Mapping:

7. Learning target #2
________________: A pair of coordinates, written in the form (x, y), used to locate any point on a coordinate plane.
________________________: composed of the x-axis (horizontal) and y-axis (vertical), which meet at the origin (0, 0) and divide the plane into four quandrants.

8. Learning target #2
Ordered Pair: A pair of coordinates, written in the form (x, y), used to locate any point on a coordinate plane.
Cartesian Coordinate Plane: composed of the x-axis (horizontal) and y-axis (vertical), which meet at the origin (0, 0) and divide the plane into four quandrants.

9. ______________: is a set of ordered pairs.
Examples:
______________: is a set of ordered pairs.
______________ (of a relation): the set of all first coordinates (x- coordinates) from the ordered pairs.
_____________ (of a relation): the set of all second coordinates (y-coordinates) from the order pairs.
Learning targets #2 & 3

10. Relation; Domain; Range
Learning targets #2 & 3
Examples:
Relation:
{ (12, 28), (15, 30), (8, 20), (12, 20), (20, 50)}
Domain:
{8, 12, 15, 20}
Range:
{20, 28, 30, 50}
Relation: is a set of ordered pairs.
Domain (of a relation): the set of all first coordinates (x-coordinates) from the ordered pairs.
Range (of a relation): the set of all second coordinates (y-coordinates) from the order pairs.

11. Function
Functions can be represented as 𝑓 𝑥 or 𝑔 𝑥 .
When speaking, we say “F of x” or “G of x”.
Learning targets #2 & 4
A ___________ is a special type of relation. Each element of the domain is paired with exactly one element of the range.
A ______________ shows how the members are paired. An example is shown to the right.
The example to the right is a function; each element of the domain is paired with exactly one element of the domain. This is called a one-to-one function.

12. Function Relation: {(12, 28), (15, 30), (8, 20)} Domain Range
Functions can be represented as 𝑓 𝑥 or 𝑔 𝑥 .
When speaking, we say “F of x” or “G of x”.
Learning targets #2 & 4
A ___________ is a special type of relation. Each element of the domain is paired with exactly one element of the range.
A ______________ shows how the members are paired. An example is shown to the right.
The example to the right is a function; each element of the domain is paired with exactly one element of the domain. This is called a one-to-one function.
Relation:
{(12, 28), (15, 30), (8, 20)}
Domain Range 12 15 8 28 30 20

13. Example #1
Learning targets #1 - 4
State the domain and range of the relation { −2, 2 , 1,4 , 3, 0 , −2, −4 , 0, 3 }. Draw a mapping. Is this relation a function?

14. Guided Practice – Example #1
Learning targets #1 - 4
State the domain and range of the relation { 7, 8 , 7, 5 , 7, 2 , 7, −1 }. Draw a mapping. Is this relation a function?
Also…try #1, 2, 3, and 8 on page 62

15. Practice Function or not?
Learning targets #2 & 4
Domain
Range
Domain
Range -3 2 1 4 -1 1 4 3 5
Domain
Range -3 1 5 6

16. Relations: Discrete or Continuous?
Learning targets #2 & 5

17. Relations: Discrete or Continuous?
Learning targets #2 & 5
Discrete
Continuous
Discrete graphs contain a set of
points not connected.
Continuous graphs contain a smooth line
or curve.
Note: You can draw the graph of a continuous relation
Without lifting you pencil from the paper.

18. Vertical Line Test
Learning targets #2 & 6

19. Vertical Line Test
Learning targets #2 & 6
If no vertical line intersects a graph in more than one point, the graph represents a function.
If some vertical line intersects a graph in two or more points, the graph DOES NOT represent a function.

20. Example #2
Learning targets #1 - 6
The number if employees a company had in each year from 1999 to were 25, 28, 34, 31, 27, and 29. Graph this information and determine whether it represents a function. Is the relation discrete or continuous?

21. Example #3 Graph the relation represented by 𝑦= 𝑥 2 +1.
Learning targets #1 - 6
Graph the relation represented by 𝑦= 𝑥 2 +1.
Find the domain and range.
Determine if the relation is discrete or continuous.
Determine whether the relation is a function.

22. Guided Practice – Examples #2&3
Learning targets #1 - 6
Page 63 #4, 5, 6, 8, 9, and 10

23. Example #4 Given 𝑔 𝑥 =0.5 𝑥 2 −5𝑥+3.5, find each value.
Learning target #7
Given 𝑔 𝑥 =0.5 𝑥 2 −5𝑥+3.5, find each value.
a. 𝑔(2.8) b. 𝑔(4𝑎)

24. Guided Practice – Example #4
Learning target #7
1. Find 𝑓 5 if 𝑓 𝑥 = 𝑥 2 −3𝑥 2. Find ℎ(−2) if ℎ 𝑥 = 𝑥 3 +1.

25. A#2.1
pages 62-63
#13-22 all;
and #24-42 evens
Due Tuesday!!!