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Algebra II: Chapter 2 Mrs. Lowerys Notes!

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Vocabulary Quiz 1. A set of pairs of input and output values 2. The x-coordinates of the relational pair 3. The y-coordinates of the relational pair 4. A way to show the relation between x & y values 5. A relation in which each element of the domain is paired with exactly one element in the range 6. A line which determines whether or not a graph is a function 7. f of x notation a. Vertical Line Test b. Mapping Diagram c. Range d. Relation e. Function Notation f. Function g. Domain Please match the following words with their definition

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Coordinate Plane and Ordered Pairs Q1 (+x, +y) QIV (+x, -y) QII (-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 1. Plot your points or Graph your Equation 2. Draw a vertical line anywhere on the quadrant plane 3. 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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Example How To Graph: 1. Identify y-intercept 2. Identify Slope 3. Graph 1. Identify y-intercept 2. Identify x-intercept Technology Application & Algebraically

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Standard Form Ax + By = C How to convert: 1. Ax must be positive 2. No Fractions 3. A, B, C must be reduced

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Standard Form Graphing How to Graph from Standard Form 1. Find x & y intercepts 2. Plot Points 3. 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) 1. Use point-slope 2. Use slope intercept

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

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Types of Lines: 1. Horizontal Lines y = # 2. Vertical Lines x = # 3. Perpendicular Lines – 1. slope =opposite, reciprocal 2. Y-intercept = any number 4. Parallel Lines – 1. Slope – Same 2. Y-intercept = any number other than original

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Assignment: P67 17, 18, 26-41, 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??? XYK = y/x XYK = y/x

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Use Proportions 1.Put problem is proportion 2.Cross Multiple 3.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 1. Weak + 2. Strong + 3. Weak – 4. Strong – 5. No Correlation

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Trend Line Line that approximates the relationship between data points (LINE OF BEST FIT) 1. Draw a line through data 2. Pick 2 points 3. Find equation 1. 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: 1.Identify b, m, c 2.Find Vertex, Plot, Label 3.Create Table 2 xs higher & 2 xs lower than x vertex 4.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 1. Solve for y 1. (Do not forget to flip sign if divide by a negative) 2. Start at y-intercept (b) 3. Plot slope (m) 4. If dotted line; If solid line 5. Shade!!

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Assignment Review Packet Ch2 Quiz 3

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