Algebra 2 Chapter 2

Algebra 2 Chapter

Algebra 2 Chapter 2112.1 Relations and FunctionsRelation Any set of inputs and outputs.Maybe represented as aTableOrdered pairsMappingGraph

22.1 Relations and FunctionsExample 1:The monthly average water temperature of the Gulf of Mexico in Key West, Florida is as follows:January69FFebruary70FMarch75FApril 78FRepresent this relation in the 4 ways.

32.1 Relations and FunctionsTableMonthTemp123469 F70 F75 F78 F42.1 Relations and FunctionsOrdered Pairs{( ), ( ), ( ), ( )} 1,692,703,754,7852.1 Relations and FunctionsMapping

123469 F70 F75 F78 F62.1 Relations and Functions3687072747678124Graph72.1 Relations and FunctionsDomain the set of inputs of a relationthe x-coordinates of the ordered pairs

Range the set of outputs of a relationthe y-coordinates of the ordered pairs

82.1 Relations and FunctionsExample 2:

Write the domain and range from example 1.

Domain: { } Range: { }

91, 2, 3, 469, 70, 75, 782.1 Relations and FunctionsFunction a relation where no input (x) repeats.102.1 Relations and FunctionsExample 3aIs the relation a function?

{(3, 5), (5, 4), (4, 6), (0, 6)}

YES!

112.1 Relations and FunctionsExample 3bIs the relation a function?

12xy543591002010NO!2.1 Relations and Functions 13456782468Example 3cIs the relation a function?

YES!2.1 Relations and Functions

14Example 4a Use the vertical line test to determine if the relation is a function.NO!2.1 Relations and Functions15Example 4b Use the vertical line test to determine if the relation is a function.

NO!2.1 Relations and Functions16Example 4c Use the vertical line test to determine if the relation is a function.

NO!2.1 Relations and Functions17Function Rule An equation that represents an output value in terms of an input value

Function Notation f(x) f(x) is read f of x.On a graph, f(x) is y.

2.1 Relations and Functions18Example 5Evaluate the function for the given values of x, and write the input x and output as an ordered pair.

a. x = 9b. x = 4

2.1 Relations and Functions19Example 5 (continued)

(9,1)

2.1 Relations and Functions20Example 5 (continued)

2.1 Relations and Functions21Assignment:

p.65 (#9 16 all, 18 24 evens)

2.1 Relations and Functions22Independent Variable Usually x, represents the input value of the function

Dependent Variable Usually f(x), represents the output value of the function (The value of this variable depends on the input value.)

2.1 Relations and Functions23Example 6To wash her brothers clothes Jennifer charges him a base rate of $15 plus $3.50 per hour. Write a function rule to model the cost of washing her brothers clothes.

2.1 Relations and FunctionsC(x) = ____ + _____ x

Then evaluate the function if it takes Jennifer 2 hours to wash his clothes.C(2.5) = 15 + 3.50(2.5)C(2.5) = 23.75Jennifer will charge $23.75.

24153.502.1 Relations and Functions25Example 7 Find the domain and range of each relation.

2.1 Relations and Functions26Example 7a

Domain: x > 0Range: ARN

2.1 Relations and Functions27Example 7b

Domain: 4 < x < 4Range: 4 < y < 4

2.1 Relations and Functions28Example 8

The relationship between your weekly salary S and the number of hours worked h is described by the following function.

2.1 Relations and Functions29Example 8 (continued)

In the following pairs, the input is the number of hours worked and the output is your weekly salary. Find the unknown measure in each ordered pair.

2.1 Relations and Functions30Example 8 (continued)

a.)

2.1 Relations and Functions31Example 8 (continued)

b.) (h, 135.20)

2.1 Relations and Functions32Assignment:

p.65-66 (#25, 26, 29 33, 39 44, 48)

2.2 Direct VariationA function where the ratio of output to input is called direct variation.332.2 Direct Variation34outputinputConstant of variation2.2 Direct VariationFor each of the following tables, determine whether y varies directly as x. If so, find the constant of variation and the equation of variation.352.2 Direct VariationExample 1

36xy1372193YES!k = 3So y = kx would mean y = 3x.2.2 Direct VariationExample 237xy 2 210 153NO! 32.2 Direct VariationExample 3If y varies directly as x, and y = 4 when x = 25. What is x when y = 10?

38 4x = 250 x = 62.5 2.2 Direct VariationExample 4If y varies directly as x, and x = 8 when y = 10, find y when x = 30.39300 = 8y 37.5 = y 2.2 Direct VariationExample 5The cost buying sirloin steak is directly proportional with the weight in pounds. If 8.5 lbs of steak cost $47.60, how much does 20 lbs cost?40=d = $1122.2 Direct VariationAssignment:

p.71(#7 10, 19 26)412.3 Linear Functions & Slope Intercept Form42

2.3 Linear Functions & Slope Intercept FormExample 1

What is the slope of the line that passes through the given points? 432.3 Linear Functions & Slope Intercept FormExample 1a

(10, 2) and (4, 5)

44

2.3 Linear Functions & Slope Intercept FormExample 1b

(6, 1) and (5, 1)

45

0 in numerator2.3 Linear Functions & Slope Intercept FormExample 1c

(2, 5) and (2, 1)

46

0 in denominatorThe slope isUNDEFINED!0 in denominator2.3 Linear Functions & Slope Intercept Form47

Assignment:p.78 (#9-15)2.3 Linear Functions & Slope Intercept FormSlope-intercept Form48

where m is the slope of the line and (0, b) is the y-intercept.2.3 Linear Functions & Slope Intercept FormExample 2

What is an equation of each line in slope-intercept form?492.3 Linear Functions & Slope Intercept formExample 2a

50

Slope = 3y-intercept is (0,5)

2.3 Linear Functions & Slope Intercept FormExample 2b

Slope =

y-intercept = 51

up 2over 32.3 Linear Functions & Slope Intercept FormExample 3 Write the equation in slope-intercept form. What are the slope and y-intercept?

522.3 Linear Functions & Slope Intercept FormExample 3a2x + 3y 15 = 0 2x 2x 3y 15 = 2x + 15 + 15 3y = 2x + 15 3 3 3

53

2.3 Linear Functions & Slope Intercept Form54

2.3 Linear Functions & Slope Intercept FormExample 3b 12 = 10y 3x+ 3x + 3x12 + 3x = 10y10 10 10

55

Slope = y-intercept =

2.3 Linear Functions & Slope Intercept FormExample 4 What is the graph of 24 = 4x + 3y?

56 24 = 4x + 3y 4x 4x 4x + 24 = 3y 3 3 3

2.3 Linear Functions & Slope Intercept FormExample 4 (continued)

57

8Assignment: 58p.78(#17-31 odds)2.3 Linear Functions & Slope Intercept FormExample 5 A horizontal line has slope 0.Graph y = 5.

m = 0 b = 5 592.3 Linear Functions & Slope Intercept FormExample 6 The slope of a vertical line is UNDEFINED. Graph x = 3.602.3 Linear Functions & Slope Intercept FormSlope = undefinedy-intercept = NONEAssignment: 61p.78(#32 52 evens)2.3 Linear Functions & Slope Intercept form2.4 More About Linear Equations

Point-slope form

62

2.4 More About Linear EquationsExample 1

Use the given information to write an equation in point-slope form.

632.4 More About Linear Equationsa. slope = through ( 1 , 3)64

2.4 More About Linear Equationsb.) slope = 0 through (22, 1)

652.4 More About Linear Equations66c.) passing through (5, 1) and (7, 1)2.4 More About Linear Equationsd.) passing through (4, 1) and ( 6, 5)672.4 More About Linear EquationsSlopes of parallel lines are equal / the same .

Slopes of perpendicular lines areoppositereciprocals.

682.4 More About Linear EquationsExample 2Use the given information to write the equation of the line described in slope-intercept form.

692.4 More About Linear Equationsa.) parallel to y = x + 2 through ( 5, 3)702.4 More About Linear Equationsb.) perpendicular to y = 2x + 3 712.4 More About Linear EquationsAssignment:p.86-88 (#10 18, 32, 33, 65, 72, 74)

722.4 More About Linear EquationsExample 3Use the given information to write the equation of the line described in slope-intercept form.

732.4 More About Linear Equationsa.) parallel to 3x 2y = 6through ( 3, 5)742.4 More About Linear Equationsb.) perpendicular to 4x + y = 1 through (2,1)752.4 More About Linear EquationsExample 4Find the intercepts, and graph the line. 762.4 More About Linear Equationsa.) 4x + 3y = 12

77

2.4 More About Linear Equationsb.) 4x 5y = 10

78

2.4 More About Linear EquationsExample 5The cost of a taxi ride depends on the distance traveled. You paid $8.50 for a 3-mile ride, and your friend paid $18.50 for an 8-mile ride792.4 More About Linear Equations80

Example 5

A.) Sketch a graph that models this situation.2.4 More About Linear EquationsExample 5 (continued)

B.) Write the equation in slope-intercept form for this situation. C.) How much would a 6 mile taxi ride cost?812.4 More About Linear EquationsAssignment:

p.86-87(#26-31,34-41)82