Algebra II: Chapter 2

Mrs. Lowery’s Notes!

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 Testb. Mapping Diagramc. Ranged. Relatione. Function Notationf. Functiong. Domain

Please match the following words with their definition

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)

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

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)

More …Is this Relation a Function?

Vertical Line Test1. Plot your points or Graph your Equation2. Draw a vertical line anywhere on the

quadrant plane3. 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)

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

Practice f(x) = x+1

Find f(3) f(4) f(6)

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

Linear Equations

What does Linear mean?

Slope – Intercept Form

y = mx + b b = y-intercept (starting point)

m = slope =

Dependent Variable Independent Variable

12

12

xx

yy

run

rise

Example

How To Graph:

1. Identify y-intercept

2. Identify Slope

3. Graph1. Identify y-intercept

2. Identify x-intercept

23

4 xy

Technology Application

&

Algebraically

Standard Form Ax + By = C

How to convert:1. Ax must be positive

2. No Fractions

3. A, B, C must be reduced

23

4 xy

Standard Form Graphing

How to Graph from Standard Form1. Find x & y intercepts

2. Plot Points

3. Connect the dots

Domain & Range of Linear Function

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

Find Slope

Use two points on a line m = slope =

12

12

xx

yy

run

rise

Point-Slope Form

)( 11 xxmyy

Insert for variables in box – y & x always are y & x

Put into Standard Form

slope = ; (22,12)

1. Use point-slope

2. Use slope intercept

6

5

Assignment

P67 1-9odd; 11-14; 21-25 odd

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

Assignment:

P67 17, 18, 26-41, 54-61 Lesson Quiz tomorrow 2.2 Chapter Quiz tomorrow

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)

Is this direct???

X Y K = y/x

-6

3

12

-2

1

4

X Y K = y/x

-1

3

6

-2

4

7

Use Proportions

2

2

1

1y

x

y

x

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

Assignment

GP P74 1, 12, 15, 20, 25 Assignment: P75 29- 47odd 52

Linear Models

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

Identify x,y variables Write equation y = mx +b

P79 extra example 1

Scatter Plot Correlations

1. Weak +

2. Strong +

3. Weak –

4. Strong –

5. No Correlation

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 equation1. Example 4 P80

Technology Application

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

Assignment

P81 13, 15, 16, 22, 23

Absolute Value Equations

cbmxy

Vertex – (min or max) (-b/m, c)

How To Graph:

1. Identify b, m, c

2. Find Vertex, Plot, Label

3. Create Table 2 x’s higher & 2 x’s lower than x vertex

4. Plot Table

Example 112 xy

Together – White Board

P90 1, 8, 10

- with calculator application

Assignment

P90 18, 20, 29-32; 33-43 odd Worksheet Quiz Ch 2. Quiz 2

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 < or > dotted line; If solid line

5. Shade!!

;

Assignment

Review Packet Ch2 Quiz 3