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

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Presentation transcript:

CHAPTER 3 GRAPHING 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 Pair  Mapping Diagram PREVIOUS VOCABULARY

 Relation  Function  Domain  Range  Independent Variable  Dependent Variable CORE VOCABULARY

 Pairs inputs with outputs  When 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 TEST  A 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 in two variables  linear function  nonlinear function  solution of a linear equation in two variables  discrete domain  continuous domain CORE VOCABULARY

 an equation that can be written in the form y = mx + b  m and b are constants  Graph is a line LINEAR EQUATION IN TWO VARIABLES

 function whose graph is a nonvertical line  has a constant rate of change  can 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 function  Quadrant PREVIOUS VOCABULARY

 Function notation CORE VOCABULARY

 f(x)  another name for y  read 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 form  x-intercept  y-intercept CORE VOCABULARY

 Ax + By = C  A, 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 Lines  Goes from left to right  Crosses the y-axis  y = a number  No slope CORE CONCEPT

 Vertical Lines  Goes up and down  Crosses the x-axis  x = a number  Slope is undefined CORE CONCEPT

 What you will learn:  Write and graph compound inequalities  Solve compound inequalities  Use 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