3.1 Relations 3.2 Graphs

Objective: Find the Cartesian product of two sets.

Find the following Cartesian products.

Objective: List ordered pairs from a Cartesian product that satisfy a given relation. Any set of ordered pairs selected from a Cartesian product is a relation.

Objective: List the domain and the range of a relation.

C {(a, 1), (b, 2), (c, 3), (e, 2)}. List the domain and the range of the relation D {(2, 2), (1, 1), (1,2), (1, 3)}.

Objective: Use set-builder notation to define a relation.

E Use the set {1, 2, 3,..., 10}.Find {x|5 < x < 7}. F Use the set Q X Q, where Q = {2, 3, 4, 5}. Find {(x, y)|x > 2 and y > 3}.

Objective: Graph ordered pairs of a relation Cartesian Coordinate System

Objective: Determine whether an ordered pair is a solution of an equation. Solution: An ordered pair such that when the numbers are substituted for the variables, a true equation is produced

Determine whether the given ordered pairs are solutions to the equation y = 3x - 1: G (7, 5) H (7, 20) I (0, 6)

Objective: Graph equations by plotting several solutions.

Graph the following relations

HW #3.1-2 Pg Odd, Pg , 31, 37, 43-57

Pg b Pg c Pg d Pg Pg a Pg Pg c Pg HW Quiz #3.1-2 Wednesday, August 26, 2015

Chapter 3 Relations, Functions, and Graphs 3.3 Functions

Objective: Recognize functions and their graphs. A relation where each member of the domain is paired with exactly one member of the range is a function.

Objective: Recognize functions and their graphs.

Which of the following relations are functions? A B

Objective: Recognize functions and their graphs.

Function Not a Function

Which of the following relations are functions? C D

Objective: Use function notation to find the value of functions. FUNCTION MACHINE Pronounced “f of x”

Objective: Use function notation to find the value of functions. FUNCTION MACHINE

Objective: Use function notation to find the value of functions.

Objective: Find the domain of a function, given a formula for the function. When the function in R X R is given by a formula, the domain is understood to be all real numbers that are acceptable replacements. Finding the domain of a function  2 rules 1. Cannot let 0 be in the denominator 2. Cannot take a square root of a negative number

Objective: Find the domain of a function, given a formula for the function.

Find the domain of the following functions. State the domain using set-builder notation

HW #3.3-4 Pg odd, Pg Odd, 11, 17, 21, 25, 27, 36-42

HW Quiz #3.3-4 Wednesday, August 26, 2015

Chapter 3 Relations, Functions, and Graphs 3.4 Graphs of Linear Functions 3.5 Slope

Objective: Find the slope of a line containing a given pair of points. Slope is the measure of how steep a line is

Objective: Find the slope of a line containing a given pair of points. Slope is the measure of how steep a line is

Objective: Find the slope of a line containing a given pair of points.

Objective: Use the point-slope equation to find an equation of a line..

HW #3.4-5 Pg Odd, 11, 17, 21, 25, 27, Pg Every Third Problem, 45-55

Chapter 3 Relations, Functions, and Graphs 3.6 More Equations of Lines

Objective: Use the two point equation to find an equation of a line..

Objective: Use the two point equation to find an equation of a line.

Objective: Find the slope and y-intercept of a line, given the slope- intercept equation for the line.

Objective: Graph linear equations in slope-intercept form.

Chapter 3 Relations, Functions, and Graphs 3.7 Parallel and Perpendicular lines

Objective: Determine if two lines are parallel or perpendicular or neither.

HW #3.6-7 Pg Every Third Problem, Pg odd, 30-32

Pg Pg Pg aPg Pg Pg Pg bPg HW Quiz #3.7 Wednesday, August 26, 2015

Chapter 3 Relations, Functions, and Graphs 3.9 More Functions

First class postage for letters or packages is a function of weight. For one ounce or less, the postage is $0.41. For each additional ounce or fraction of an ounce, $0.41 is due. 1.What is the postage for a 0.5 oz package? 2.What is the postage for a 0.7 oz package? 3.What is the postage for a 1 oz package? 4.What is the postage for a 1.5 oz package? 5.What is the postage for a 2 oz package? 6.What is the postage for a 2.5 oz package? 7.Sketch a graph of the weight of the package vs cost to ship

A step function has a graph which resembles a set of stair steps. Objective: Graph special functions Another example of a step function is the greatest integer function f(x) = [x]. The greatest integer function, f(x) = [x], is the greatest integer that is less than or equal to x.

Objective: Graph special functions

Finding the absolute value of a number can also be thought of in terms of a function, the absolute value function, f(x) = |x|.

Objective: Graph special functions

Sketch the graph of the following two functions

Objective: Find the composite of two functions

For f(x) = 3x + b and g(x) = 2x – 7 find f(g(x)) For f(x) = px + d find f(f(x)) For f(x) = 2x + 6 and g(x) = 3x + b find b such that f(g(x)) = g(f(x))

HW #3.9 Pg Odd, 26-51

Pg aPg Pg Pg Pg bPg Pg Pg HW Quiz #3.9 HW Quiz #3.9 Wednesday, August 26, 2015

Chapter 3 Relations, Functions, and Graphs 3.8 Mathematical Modeling: Using Linear Functions

Objective: Find a linear function and use the equation to make predictions A scatter plot is a graph used to determine whether there is a relationship between paired data. When data show a positive or negative correlation,you can approximate the data with a line.

A B

Crickets are known to chirp faster at higher temperatures and slower at lower temperatures. The number of chirps is thus a function of the temperature. The following data were collected and recorded in a table. Objective: Find a linear function and use the equation to make predictions Use the data collected in the table to predict the number of chirps per minute when the temperature is 18°C.

Objective: Find a linear function and use the equation to make predictions Find the line through (6, 11) and (15, 75) and use the line to predict the number of chirps at 18.

Objective: Find a linear function and use the equation to make predictions

C In 1950 natural gas demand in the United States was 20 quadrillion joules. In 1960 the demand was 22 quadrillion joules. Let D represent the demand for natural gas t years after Fit a linear function to the data points. D Use the function to predict the natural gas demand in 2004

HW #3.8 Pg Odd, 14-16

HW Quiz #3.8 Wednesday, August 26, 2015

Test Review Objective: List the domain and the range of a relation. Objective: Recognize functions and their graphs. Objective: Use function notation to find the value of functions. Objective: Find the domain of a function, given a formula for the function. Objective: Find the slope of a line containing a given pair of points. Objective: Use the point-slope equation to find an equation of a line. Objective: Graph linear equations in slope-intercept form. Objective: Find the slope and y-intercept of a line, given the slope- intercept equation for the line. Objective: Determine if two lines are parallel or perpendicular or neither. Objective: Graph special functions Objective: Find the composite of two functions Objective: Find a linear function and use the equation to make predictions

Part 1

For f(x) = 3x + b and g(x) = 2x – 7 find f(g(x)) For f(x) = px + d find f(f(x)) For f(x) = 2x + 6 and g(x) = 3x + b find b such that f(g(x)) = g(f(x)) Given that f is a linear function with f(4)=-5 and f(0) = 3, write the equation that defines f.

Part 2

Show that the line containing the points (a, b) and (b, a) is perpendicular to the line y = x. Also show that the midpoint of (a, b) and (b, a) lies on the line y = x. The equation 2x – y = C defines a family of lines, one line for each value of C. On one set of coordinate axes, graph the members of the family when C = -2, C= 0, and C= 4. Can you draw any conclusion from the graph about each member of the family? What about Cx +y = -4? If two lines have the same slope but different x-intercepts, can they have the same y-intercept? If two lines have the same y-intercept, but different slopes, can they have the same x-intercept?

The Greek method for finding the equation of a line tangent to a circle used the fact that at any point on a circle the line containing the center and the tangent line are perpendicular. Use this method to find the equation of the line tangent to the circle x 2 + y 2 = 9 at the point (1, 2  2). Prove: If c  d and a and b are not both zero, then ax + by =c and ax + by = d are parallel

HW #R-3 Pg Study all challenge problems

Find the area of an equilateral triangle