CHAPTER 3 GRAPHING LINEAR FUNCTIONS What you will learn: Determine whether relations are functions Find the domain and range of a functions Identify.

CHAPTER 3GRAPHING LINEAR

FUNCTIONS

What you will learn:Determine whether relations are functions

Find the domain and range of a functions

Identify the independent and dependent variable functions

3.1 FUNCTION

What is a function?

ESSENTIAL QUESTION

Ordered PairMapping Diagram

PREVIOUS VOCABULARY

RelationFunctionDomainRangeIndependent Variable

Dependent Variable

CORE VOCABULARY

Pairs inputs with outputsWhen given as an ordered pairs, the x-

coordinates are inputs and the y-coordinates are outputs

RELATION

A relation that pairs each input with exactly one output

FUNCTION

The set of all possible input values

DOMAIN

The set of all possible output values

RANGE

The variable that represents the input values of a function

It can be any value in the domain

INDEPENDENT VARIABLE

VERTICAL LINE TESTA graph is a function when no vertical line passes through more than one point on the graph

CORE CONCEPT

What you will learn: Identify linear functions using graphs, tables, and equations

Graph linear functions using discrete and continuous data

Write real-life problems to fit data

3.2 LINEAR FUNCTIONS

How can you determine whether a function is linear or nonlinear?

LEAVE 4 LINES

ESSENTIAL QUESTION:

linear equation intwo variables

linear functionnonlinear function

solution of a

linear equation in two variables

discrete domaincontinuous domain

CORE VOCABULARY

an equation that can be written in the form y = mx + b

m and b are constantsGraph is a line

LINEAR EQUATION IN TWO VARIABLES

function whose graph is a nonvertical line

has a constant rate of changecan be represented by a linear equation in two variables

LINEAR FUNCTION

does not have a constant rate of change

its graph is not a line.

NONLINEAR FUNCTION

an ordered pair (x, y) that makes the equation true

The graph is the set of points (x, y) in a coordinate plane that represents all solutions of the equation

SOLUTION OF A LINEAR EQUATON IN TWO VARIABLES

set of input values that consists of only certain numbers in an interval

DISCRETE DOMAIN

set of input values that consists of all numbers in an interval

FUNCTION NOTATION

What you will learn:Function notation to evaluate and interpret functions

Use function notation to solve and graph functions

Solve real-life problems using function notation

3.3 FUNCTION NOTATION

How can you use function notation to represent a function?

LEAVE 4 LINES

ESSENTIAL QUESTION:

Linear functionQuadrant

PREVIOUS VOCABULARY

Function notation

CORE VOCABULARY

f(x)another name for yread as “the value of f at x” read as “f of x.” g, h, j, and k are also used

FUNCTION NOTATION

Multiplication and Division Properties of Inequality

When multiplying or dividing each side of an inequality by the same negative number, the direction of the inequality symbol must be reversed to produce an equivalent inequality.

CORE CONCEPT

What you will learn:

Graph equations of horizontal and vertical lines

Graph linear equations in standard form using intercepts

Use linear equations in standard form to solve real-life problems

3.4 GRAPHING LINEAR EQUATIONS IN STANDARD FORM

How can you describe the graph of the equation Ax + By = C?

LEAVE 4 LINES

ESSENTIAL QUESTION:

Ordered Pair

Quadrant

PREVIOUS VOCABULARY

Standard formx-intercepty-intercept

CORE VOCABULARY

Ax + By = CA, B, and C are numbers

A and B do not equal 0

STANDARD FORM

Where the graph crosses the x-axis

Y=0(x,0)

X-INTERCEPT

Where the graph crosses the y-axis

x=0(0,y)

Y-INTERCEPT

Horizontal LinesGoes from left to rightCrosses the y-axisy = a numberNo slope

CORE CONCEPT

Vertical LinesGoes up and downCrosses the x-axisx = a numberSlope is undefined

CORE CONCEPT

What you will learn:

Write and graph compound inequalities

Solve compound inequalitiesUse compound inequalities to solve real life problems

2.5 SOLVING COMPOUND INEQUALITIES

How can you use inequalities to describe intervals on the real number line?

ESSENTIAL QUESTION

Compound inequalities

VOCABULARY

Formed by joining two inequalities with the word “and” or “or”

COMPOUND INEQUALITIES

Compound inequalities “and”“and” is the intersection of the inequalities

“and” contains the solutions that are the same in both inequalities

CORE CONCEPT

Graphing Compound inequalities “or”“or” is the union of the inequality’s solutions

“or” contains all the solutions for both inequalities

CORE CONCEPT

What you will learn:

2.6 ABSOLUTE VALUE EQUATIONS

How can you solve an solve an absolute value equation?

ESSENTIAL QUESTION:

Compound inequality (2.5)

Mean (1.2)

PREVIOUS VOCABULARY

Absolute value inequality

Absolute deviation

CORE VOCABULARY

An inequality that contains and absolute value expression

ABSOLUTE VALUE INEQUALITY

Absolute value of the difference of x and the given number

ABSOLUTE DEVIATION