Algebra 2 Monday, 9/22/141. Warm-ups: pre-req skills needed for Chapter 2 (pg 57 #1-19 all)

2. Discussion/Notes/Guided Practice: 2.1 Relations and Functions

3. HW: A#2.1 pages 62-63 #13-22 all; and #24-42 evens -- due Tues

UPCOMING QUIZ and TEST DATES:Wed 10/1: Quiz - Sections 2.1 - 2.4

WARM-UPS: Complete page 57 #1-19 allwrite your answers on this page

1. Identify the BIG Ideas for Chapter 2

2. Define key vocabulary terms for Section 2.1

3. Analyze and graph relations

4. Determine if a relation is a function

5. Determine if a graph is discrete or continuous

6. Understand and use the vertical line test to determine if a graph is a function

7. Find functional values

Success Criteria: Q&A, Guided Practice Problems, HW

Preview of Chapter 2Linear Relations and Functions

Use your textbook and identify the five “BIG Ideas” for Chapter 2:1.

2.

3.

4.

5.

Learning target #1

Preview of Chapter 2Linear Relations and Functions

1. Analyze relations and functions

2. Identify, graph, and write linear equations

3. Find the slope of a line

4. Draw scatter plots and find prediction equations

5. Graph special functions, linear inequalities, and absolute value inequalities

Vocabulary for this section – How many do you already know?

• Ordered pair:

• Cartesian coordinate plane:

• Quandrant:

• Relation:

• Domain:

• Range:

• Function:

• Mapping:

• One-to-one function:

• Discrete function:

• Continuous function:

• Vertical line test:

• Independent variable:

• Dependent variable:

• Function notation:

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.

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.

Learning target #2

• ______________: 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.

Examples:

Learning targets #2 & 3

Relation; Domain; Range

• 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.

Examples:• Relation:{ (12, 28), (15, 30), (8, 20), (12, 20), (20, 50)}

• Domain:{8, 12, 15, 20}

• Range:{20, 28, 30, 50}

Learning targets #2 & 3

Function

• 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.

Functions can be represented as When speaking, we say “F of x” or “G of x”.

Learning targets #2 & 4

Function

• 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

Functions can be represented as When speaking, we say “F of x” or “G of x”.

Learning targets #2 & 4

12

15

8

28

30

20

Example #1

• State the domain and range of the relation . Draw a mapping. Is this relation a function?

Learning targets #1 - 4

Guided Practice – Example #1

• State the domain and range of the relation . Draw a mapping. Is this relation a function?

Learning targets #1 - 4

Also…try #1, 2, 3, and 8 on page 62

Practice Function or not?

-3

0

2

1

2

4

-1

1

4

3

5

-3

1

5

0

1

6

Domain Domain

Domain

Range Range

Range

Learning targets #2 & 4

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

Relations: Discrete or Continuous?

Discrete Continuous

Discrete graphs contain a set of points not connected.

Continuous graphs contain a smooth lineor curve.

Note: You can draw the graph of a continuous relationWithout lifting you pencil from the paper.

Learning targets #2 & 5

Vertical Line TestLearning targets #2 & 6

Vertical Line Test

• 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.

Learning targets #2 & 6

Example #2

• The number if employees a company had in each year from 1999 to 2004 were 25, 28, 34, 31, 27, and 29. Graph this information and determine whether it represents a function. Is the relation discrete or continuous?

Learning targets #1 - 6

Example #3

• Graph the relation represented by .

• Find the domain and range.

• Determine if the relation is discrete or continuous.

• Determine whether the relation is a function.

Learning targets #1 - 6

Guided Practice – Examples #2&3

• Page 63 #4, 5, 6, 8, 9, and 10

Learning targets #1 - 6

Example #4

• Given , find each value.

a. b.

Learning target #7

Guided Practice – Example #4

1. Find if 2. Find if .

Learning target #7

A#2.1

pages 62-63

#13-22 all; and #24-42 evens

Due Tuesday!!!