UPCOMING QUIZ and TEST DATES: Wed 10/1: Quiz - Sections 2.1 - 2.4 Algebra 2 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 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 all write your answers on this page

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

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

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

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:

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.

______________: 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

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.

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.

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

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?

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

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

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

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.

Vertical Line Test Learning targets #2 & 6

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.

Example #2 Learning targets #1 - 6 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?

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.

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

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)

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.

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