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Algebra II: Chapter 2 Mrs. Lowery’s Notes!

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**Vocabulary Quiz Please match the following words with their definition**

A set of pairs of input and output values The x-coordinates of the relational pair The y-coordinates of the relational pair A way to show the relation between x & y values A relation in which each element of the domain is paired with exactly one element in the range A line which determines whether or not a graph is a function f of x notation Vertical Line Test Mapping Diagram Range Relation Function Notation Function Domain

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**Coordinate Plane and Ordered Pairs**

Q1 (+x, +y) QII (-x, +y) QIV (+x, -y) QIII (-x, -y) Please Plot (1,5) (2,6) (3, 7)

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**Terminology Please put the ordered pairs from the previous slide in:**

Relation form (input values output) Identify the Domain (x-values) Identify the Range (y-values) Create a Mapping Diagram

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**Is the Relation a Function???**

Check out the Domain! Picture view - Mapping diagram Only 1 arrow coming out of each x Practice (-2,-1) (0,3) (-2,3) (5,4) Practice (2,6) (3,6) (4,5) (7,8)

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**More … Is this Relation a Function?**

Vertical Line Test Plot your points or Graph your Equation Draw a vertical line anywhere on the quadrant plane Count the number of times it cross the points or graph If only 1 – YES!!! It is a function If more than 1 – NO It is not a function (Practice P58 Quick Check 5)

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**Function Notation f(x)**

f(x)= (Spoken f of x) Whatever variable or number is right there plug in for the variable. Student paycheck example – How much will your paycheck be if you work????? - by hand - advanced grapher - Calculator

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Practice f(x) = x+1 Find f(3) f(4) f(6)

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Assignment Guided Practice – in groups of 2 or 3 must show me before you leave! P59 1, 6, 9, 12, 13, 20, 23 (paper or white board) Homework – P33-41odd; 43-45; 46, 50, 53

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Linear Equations What does Linear mean?

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**Slope – Intercept Form y = mx + b b = y-intercept (starting point)**

m = slope = Dependent Variable Independent Variable

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**Technology Application**

Example How To Graph: Identify y-intercept Identify Slope Graph Identify x-intercept Technology Application & Algebraically

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**Standard Form Ax + By = C How to convert: Ax must be positive**

No Fractions A, B, C must be reduced

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**Standard Form Graphing**

How to Graph from Standard Form Find x & y intercepts Plot Points Connect the dots

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**Domain & Range of Linear Function**

Domain – (x-values) Range – (y-values)

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Find Slope Use two points on a line m = slope =

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Point-Slope Form Insert for variables in box – y & x always are y & x

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**Put into Standard Form slope = ; (22,12) Use point-slope**

Use slope intercept

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Assignment P67 1-9odd; 11-14; odd

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**Types of Lines: Horizontal Lines y = # Vertical Lines x = #**

Perpendicular Lines – slope =opposite, reciprocal Y-intercept = any number Parallel Lines – Slope – Same Y-intercept = any number other than original

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**Assignment: P67 17, 18, 26-41, 54-61 Lesson Quiz tomorrow 2.2**

Chapter Quiz tomorrow

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**Direct Variation y = kx K – slope Notice no b so starts at 0**

y varies constantly with x GOAL: FIND A SPECIFIC K (0,0)

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Is this direct??? X Y K = y/x -1 3 6 -2 4 7 X Y K = y/x -6 3 12 -2 1 4

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**Use Proportions Put problem is proportion Cross Multiple Divide**

Practice 1: y = 4 when x = 3; now find y when x = 6 Practice 2: y = 15 when x = 27; now find y when x = 18

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Assignment GP P74 1, 12, 15, 20, 25 Assignment: P odd 52

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**Linear Models Linear??? – Line! Solve a problem using a linear graph**

Identify x,y variables Write equation y = mx +b P79 extra example 1

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**Scatter Plot Correlations**

Weak + Strong + Weak – Strong – No Correlation

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**Trend Line Line that approximates the relationship between data points**

(LINE OF BEST FIT) Draw a line through data Pick 2 points Find equation Example 4 P80

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**Technology Application**

Stat: edit: L1 & L2 Stat: calc – LinReg Turn scatter plot on

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Assignment P81 13, 15, 16, 22, 23

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**Absolute Value Equations**

Vertex – (min or max) (-b/m, c) How To Graph: Identify b, m, c Find Vertex, Plot, Label Create Table 2 x’s higher & 2 x’s lower than x vertex Plot Table Example

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Together – White Board P90 1, 8, 10 - with calculator application

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Assignment P90 18, 20, 29-32; odd Worksheet Quiz Ch 2. Quiz 2

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**Graphing Inequalities**

It is just like graphing linear equations Solve for y (Do not forget to flip sign if divide by a negative) Start at y-intercept (b) Plot slope (m) If < or > dotted line; If solid line Shade!!

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Assignment Review Packet Ch2 Quiz 3

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