Unit 2 Linear Relations and Functions2.1 Find the domain and range of a relation. Determine whether a relation is a function.

2.1 Evaluate a function given function notation, f(x).

2.2 Identify linear relations and functions.

2.2 Write linear equations in standard form.

2.2 Graph an equation using x and y-intercepts.

2.3 Find the rate of change and determine the slope of a line.

2.4 Write an equation of a line given the slope and a point on the line.

2.4 Write an equation of a line parallel or perpendicular to a given line.

2.5 Use scatter plots and prediction equations.

2.5 Model data using lines of regression.

Monday Tuesday Wednesday Thursday FridayAugust 24 25 26 27 28School Holiday

Ch. 1 Review Ch. 1 Test Notes 2.1 Notes 2.1

31 September 1 2 3 4Notes 2.2 Notes 2.3 Quiz 2.1-2.3 Notes 2.4 Notes 2.4

7 8 9 10 11Notes 2.4/2.5 Notes 2.5 Go Over

Quiz/Notes 2.5

2.1-2.5 Review

Test 2.1-2.5

Notes 2.1 Relations and Functions

Identifying Domain and Range:

Domain: _________________________________________________________________________________

How do we read domain on a graph? ________________________________________________________

Range: ___________________________________________________________________________________

How do we read range on a graph? ________________________________________________________

Example:

Other Words for…….

DOMAIN: RANGE:

____________________________ ____________________________

____________________________ ____________________________

What is a function?A function is a relation in which each element of the domain is paired with exactly one element in the range.

!!!!!!!!!!!!!!!!!!!!!!!!!!……..THE DOMAIN CAN’T REPEAT PEOPLE………!!!!!!!!!!!!!!!!!!!!!!!!!!!!

{(-6, -1), (-5, -9), (-3, -7), (-1, 7), (-6, -9)} {(-6, -1), (-5, -9), (-3, -7), (-1, 7), (6, -9)}

You can also use the _________________________________________________ to determine whether the relation is a function.

X Y X Y

Equations that represent functions are often written in function notation.

Given f ( x )=2 x2−8∧g (x )=0.5x2−5 x+3.5 , find eachvalue .

f (6 )=¿ f (2 y )=¿

g (4 a )=¿

Notes 2.2 Linear Relations and Functions

Relations that have straight line graphs are called linear relations.

Linear equations can be written in the form y = mx +b or ax +by = c

State whether each function is a linear function. Write yes or no, then explain why.

a. f ( x )=8−34x

__________________________________________________________________________________________

b. f ( x )=2x

__________________________________________________________________________________________

c. g ( x , y )=3 x−4 __________________________________________________________________________________________

STANDARD FORM of a Linear Equation

Write each equation in standard form. Identify A, B, and C.

x

y

a. 3 x−6 y−9=0 b. 2 y=4 x+5

c. −310x=8 y−15

Using Intercepts to Graph a Line

Find the x-intercept and the y-intercept of the graph of 2x – 3y +8 = 0. Then graph the equation.

Standard Form: _____________________________

x- intercept: _________________

\y-intercept: _________________

Notes 2.3 Rate of Change and Slope

SLOPE FOLDABLE:

Notes 2.4 Writing Linear EquationsTHE THREE FORMS FOR LINEAR EQUATIONS:

1. SLOPE INTERCEPT FORM: y=mx+b2. POINT-SLOPE FORM: y− y1=m(x−x1)3. STANDARD FORM: Ax+By=C

THE POINT-SLOPE FORMULA GENERATES THE SLOPE-INTERCEPT FORMULA WHEN YOU PERFORM YOUR ALGEBRA CORRECTLY. WE WILL ALWAYS START WITH THE POINT-SLOPE TO GENERATE THE SLOPE-INTERCEPT FORMULA.

x

y

WRITING EQUATIONS OF LINES:

(a) FROM A GRAPH: Find the slope from the graph. Plug the slope and a point into the POINT-SLOPE FORMULA.

(b) GIVEN TWO OR MORE POINTs: Use the two points to calculate the slope. Plug the slope and a point into the POINT-SLOPE FORMULA. f (-6) = -3f (-2) = 1

(c) GIVEN A SLOPE AND A POINT: Simply plug the slope and a point into the POINT-SLOPE FORMULA.

Write the equation of a line going through point (11,16) with a slope of 53

.

PARALLEL AND PERPENDICULAR LINES:Lines that are parallel have the same slope but Lines that are perpendicular have slopes that are different y-intercepts: opposite sign reciprocals:

EX: y=2x+2 and 12y=x+ 7

2 EX: y=3

2x+2 and 3 y=−2 x+6

NOTE: HORIZONTAL AND VERTICAL LINES ARE ALWAYS PERPENDICULAR:

Ex: Write an equation in Slope-Intercept Form:

1. Parallel to y=32x+6 and goes through P(4,5).

2. Perpendicular to y=−34x+2 and goes through P(6 ,−4 ).

Notes 2.5 Scatter Plots and Lines of RegressionREGRESSION – The study of the relationship between variables.

CORRELATION – The strength and the direction of the relationship between two variables.

LINE OF BEST FIT – If there is a strong relationship – A line that "best fits" the data.

CORRELATION COEFFICIENT (r) – The measure of how well the data is correlated or fits the model

-1 ≤ r ≤ 1 |r| close to 1 |r| close to 0

EX: Anthropologists can use the femur, or thighbone, to estimate the height of a human being. The table shows the results of a randomly selected sample.

Femur Length and Height(cm)

Height Length

160 36

143 32

187 46

142 29

161 35

164 38

140 30

131 27

a) Using a straightedge, draw what you think is the line of best fit on your scatterplot. What is the equation of your line? Show your work in the space below.

b) Use your graphing calculator to find the line of best fit: ___________________________________c) Interpret the slope of the line of best fit in the context of the problem.

d) Find the correlation coefficient r: ___________e) What does r tell you about this model?

f) A man’s femur is 41 cm long (this is a specific value for the independent variable). Predict the man’s height. Is this a reasonable prediction?

EX: Below are some data on the number of texts 8 students sent in one day and the number of Facebook friends they have. Make a scatter plot of the data with the number of texts as the independent variable.

Texts Facebook Friends

100 199

20 235

15 423

300 1102

50 646

76 1459

107 531

62 755

a) Find the correlation coefficient and the equation of the line of best fit using your calculator. Draw the line of best fit on your scatter plot.

b) Predict the number of Facebook friends for someone who made 250 texts in a day. How accurate do you think your prediction is?

TO GET R TO APPEAR IN THE OUTPUT: TURN DIAGNOSTICS ON

2nd “0” [CATALOG]; type Alpha “D” and scroll down to “DiagnosticOn”; hit ENTER twice

CALCULATOR INSTRUCTIONS: TO FIND THE LINE OF BEST FIT

Make sure diagnostics are turned on first.STAT – EDIT – enter the independent variable in L1 and the dependent variable in L2STAT – CALC - #4 (LinREG); “LinReg(ax+b)” will appear on the home screenBefore you hit ENTER, type Y1 (VARS – YVARS - #1Function – Y1) - This will automatically put the regression line in Y1. Now hit “ENTER”.