Chapter 4.1 Graphing Relationships
Lesson Objectives:
- Match simple graphs with situations
- Graph a relationship
Notes Part 1 |
Notes Part 2 |
Notes Part 3 |
Classwork 4.1Pg. 233 # 1-9
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Chapter 4 Standards
Florida State Standards
MA.912.A.3.1
Solve linear equations in one variable that include simplifying algebraic expressions.
MA.912.A.3.2
Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality.
MA.912.A.3.4
Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution.
MA.912.A.3.5
Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.
MA.912.A.2.1
Create a graph to represent a real-world situation.
MA.912.A.2.2
Interpret a graph representing a real-world situation.
MA.912.A.2.3
Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions.
MA.912.A.2.4
Determine the domain and range of a relation.
MA.912.A.2.7
Perform operations (addition, subtraction, division, and multiplication) of functions algebraically, numerically, and graphically.
MA.912.A.2.8
Determine the composition of functions.
MA.912.A.2.9
Recognize, interpret, & graph functions defined piece-wise
MA.912.A.2.10
Describe and graph transformations of functions
MA.912.A.2.12
Solve problems using direct, inverse, and joint variations.
MA.912.A.2.13
Solve real-world problems involving relations and functions.
Common Core State Standards
CCSS.MATH.CONTENT.HSF.IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of fcorresponding to the input x. The graph of f is the graph of the equation y = f(x).
CCSS.MATH.CONTENT.HSF.IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
CCSS.MATH.CONTENT.HSF.IF.A.3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
CCSS.MATH.CONTENT.HSF.IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
CCSS.MATH.CONTENT.HSF.IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
CCSS.MATH.CONTENT.HSF.IF.B.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
CCSS.MATH.CONTENT.HSF.IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
CCSS.MATH.CONTENT.HSF.BF.A.1
Write a function that describes a relationship between two quantities.
CCSS.MATH.CONTENT.HSF.BF.A.2
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
MA.912.A.3.1
Solve linear equations in one variable that include simplifying algebraic expressions.
MA.912.A.3.2
Identify and apply the distributive, associative, and commutative properties of real numbers and the properties of equality.
MA.912.A.3.4
Solve and graph simple and compound inequalities in one variable and be able to justify each step in a solution.
MA.912.A.3.5
Symbolically represent and solve multi-step and real-world applications that involve linear equations and inequalities.
MA.912.A.2.1
Create a graph to represent a real-world situation.
MA.912.A.2.2
Interpret a graph representing a real-world situation.
MA.912.A.2.3
Describe the concept of a function, use function notation, determine whether a given relation is a function, and link equations to functions.
MA.912.A.2.4
Determine the domain and range of a relation.
MA.912.A.2.7
Perform operations (addition, subtraction, division, and multiplication) of functions algebraically, numerically, and graphically.
MA.912.A.2.8
Determine the composition of functions.
MA.912.A.2.9
Recognize, interpret, & graph functions defined piece-wise
MA.912.A.2.10
Describe and graph transformations of functions
MA.912.A.2.12
Solve problems using direct, inverse, and joint variations.
MA.912.A.2.13
Solve real-world problems involving relations and functions.
Common Core State Standards
CCSS.MATH.CONTENT.HSF.IF.A.1
Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of fcorresponding to the input x. The graph of f is the graph of the equation y = f(x).
CCSS.MATH.CONTENT.HSF.IF.A.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
CCSS.MATH.CONTENT.HSF.IF.A.3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
CCSS.MATH.CONTENT.HSF.IF.B.4
For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
CCSS.MATH.CONTENT.HSF.IF.B.5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
CCSS.MATH.CONTENT.HSF.IF.B.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
CCSS.MATH.CONTENT.HSF.IF.C.9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
CCSS.MATH.CONTENT.HSF.BF.A.1
Write a function that describes a relationship between two quantities.
CCSS.MATH.CONTENT.HSF.BF.A.2
Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.