chapter 3 graphing linear functions what you will learn: determine whether relations are functions...
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CHAPTER 3GRAPHING LINEAR
FUNCTIONS
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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
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What is a function?
ESSENTIAL QUESTION
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Ordered PairMapping Diagram
PREVIOUS VOCABULARY
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RelationFunctionDomainRangeIndependent Variable
Dependent Variable
CORE VOCABULARY
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Pairs inputs with outputsWhen given as an ordered pairs, the x-
coordinates are inputs and the y-coordinates are outputs
RELATION
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A relation that pairs each input with exactly one output
FUNCTION
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The set of all possible input values
DOMAIN
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The set of all possible output values
RANGE
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The variable that represents the input values of a function
It can be any value in the domain
INDEPENDENT VARIABLE
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VERTICAL LINE TESTA graph is a function when no vertical line passes through more than one point on the graph
CORE CONCEPT
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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
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How can you determine whether a function is linear or nonlinear?
LEAVE 4 LINES
ESSENTIAL QUESTION:
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linear equation intwo variables
linear functionnonlinear function
solution of a
linear equation in two variables
discrete domaincontinuous domain
CORE VOCABULARY
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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
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function whose graph is a nonvertical line
has a constant rate of changecan be represented by a linear equation in two variables
LINEAR FUNCTION
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does not have a constant rate of change
its graph is not a line.
NONLINEAR FUNCTION
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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
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set of input values that consists of only certain numbers in an interval
DISCRETE DOMAIN
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set of input values that consists of all numbers in an interval
FUNCTION NOTATION
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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
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How can you use function notation to represent a function?
LEAVE 4 LINES
ESSENTIAL QUESTION:
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Linear functionQuadrant
PREVIOUS VOCABULARY
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Function notation
CORE VOCABULARY
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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
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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
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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
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How can you describe the graph of the equation Ax + By = C?
LEAVE 4 LINES
ESSENTIAL QUESTION:
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Ordered Pair
Quadrant
PREVIOUS VOCABULARY
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Standard formx-intercepty-intercept
CORE VOCABULARY
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Ax + By = CA, B, and C are numbers
A and B do not equal 0
STANDARD FORM
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Where the graph crosses the x-axis
Y=0(x,0)
X-INTERCEPT
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Where the graph crosses the y-axis
x=0(0,y)
Y-INTERCEPT
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Horizontal LinesGoes from left to rightCrosses the y-axisy = a numberNo slope
CORE CONCEPT
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Vertical LinesGoes up and downCrosses the x-axisx = a numberSlope is undefined
CORE CONCEPT
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What you will learn:
Write and graph compound inequalities
Solve compound inequalitiesUse compound inequalities to solve real life problems
2.5 SOLVING COMPOUND INEQUALITIES
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How can you use inequalities to describe intervals on the real number line?
ESSENTIAL QUESTION
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Compound inequalities
VOCABULARY
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Formed by joining two inequalities with the word “and” or “or”
COMPOUND INEQUALITIES
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Compound inequalities “and”“and” is the intersection of the inequalities
“and” contains the solutions that are the same in both inequalities
CORE CONCEPT
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Graphing Compound inequalities “or”“or” is the union of the inequality’s solutions
“or” contains all the solutions for both inequalities
CORE CONCEPT
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What you will learn:
2.6 ABSOLUTE VALUE EQUATIONS
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How can you solve an solve an absolute value equation?
ESSENTIAL QUESTION:
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Compound inequality (2.5)
Mean (1.2)
PREVIOUS VOCABULARY
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Absolute value inequality
Absolute deviation
CORE VOCABULARY
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An inequality that contains and absolute value expression
ABSOLUTE VALUE INEQUALITY
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Absolute value of the difference of x and the given number
ABSOLUTE DEVIATION
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