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Lafayette Parish School System Advanced Math Functions Curriculum Map Unit 2: Functions and Their Graphs CC# Common Core Evidence / Assessments of learning Instructional Notes/Strategies Differentiation Student Understandings F.IF.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 f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F.IF.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.★ F.IF.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 personhours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.* F.IF.6 Calculate and interpret the average rate of Introduction to Functions Graphs of Functions Transformation of Graphs Operations on Functions Composition of Functions Inverse Functions One-to-Functions Determine whether a relation is a function Find the domain of a function Determine a graph to be a function Determine where a graph is increasing, decreasing, and constant Use a graph to locate local maxima and minima Determine even and odd functions from a graph and an equation How is the domain and range of a function, determined from a graph of a function? Find the domain of an equation. 2.1 Functions 2.3 Properties of Functions Math 105 4.1-4.5;8.1 Lafayette Parish School System Advanced Math Functions Curriculum Map Unit 2: Functions and Their Graphs CC# Common Core Evidence / Assessments of learning Instructional Notes/Strategies Differentiation change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★ F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima. F.IF.7b Graph square root, cube root, and piecewisedefined functions, including step functions and absolute value functions. F.IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. F.BF.1 F.IF.7 F.BF.3 F.BF.1 Write a function that describes a relationship between two quantities. Graph functions expressed symbolically and show key features of the graph, by hand in the simple cases and using technology for more complicated cases. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. Write a function that describes a relationship Determine parent functions Transform graphs of parent functions What happens to a parent function when you transform its graph? 2.4 Library of Functions 2.5 Graphing Techniques: Transformations Math 105 8.3 TI NSpire CX Activity: Algebra 2: Families of Functions TI NSpire CX Activity: Precalculus: Slider Template TI NSpire CX Activity: Algebra 2: Transformations: Dilating Functions TI NSpire CX Activity: Algebra 2: Transformations: Translating Functions TI NSpire CX Activity: Algebra 2: Graphic Designing with Transformed Functions Form sum, difference , product, and 2.6 Operations on Math 105 8.2 Lafayette Parish School System Advanced Math Functions Curriculum Map Unit 2: Functions and Their Graphs CC# Common Core between two quantities. Evidence / Assessments of learning quotient of functions and find their domain Form composite functions and find their domain Can students combine two functions using the operations of addition, subtraction, multiplication, and division? Can students find and use compositions of functions? F.IF.2 F.IF.5 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. 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.★ Instructional Notes/Strategies Functions Differentiation Math TV (Select:Algebra>Functions>Algebra with Functions) Illustrative Mathematics: A Sum of Functions Math Insight: Visual of Function Machine Compostion Math is Fun: Composition of Functions Purplemath: Composition of Functions F.IF.7 Regents Prep: Compostion of Functions Graph functions expressed symbolically and show key features of the graph, by hand in the simple cases and using technology for more complicated cases. ck-12 Foundation: Composite Functions Math TV (Select: Algebra>Functions>Composition Illustrative Mathematics: Flu on Campus TI NSpire CX Activity: Algebra 2: Function Composition TI NSpire CX Activity: Algebra 2: Application of Function Composition F.IF.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 f corresponding to the input x. The graph of f is the graph of the equation y = f(x). Define inverse relations and functions Find inverse relations from tables, graphs, and equations Determine whether an inverse relation is a function What is the algebraic process that is used to find the inverse of a function? Can students verify that two functions are 4.1 One-to-one and Inverse functions Math 105 8.4 ck-12 Foundation: One-to-One Functions and Their Inverses ck-12 Foundation: Functions and Inverses Regents Prep: Inverse Functions Lafayette Parish School System Advanced Math Functions Curriculum Map Unit 2: Functions and Their Graphs CC# Common Core F.IF.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.★ F.BF.4 Find inverse functions. F.BF.4a Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x–1) for . Evidence / Assessments of learning inverses of each other? Instructional Notes/Strategies Differentiation Math TV (select: Algebra>Functions>Inverse Functions) Illustrative Mathematics: Graphs of Compositions Illustrative Mathematics: Invertible or Not? Illustrative Mathematics: Rainfall Illustrative Mathematics: Temperature Conversions Illustrative Mathematics: US Households F.BF.4b Verify by composition that one function is an inverse of another. Shmoop: Examples of Math.F.BF.4 F.BF.4c Read values of an inverse function from a graph or table, given that the function has an inverse. TI NSpire CX Activity: Algebra 2: Functions and Inverses F.BF.4d Produce an invertible function from a noninvertible function by restricting a domain.