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