High School Math Guide

Features of Functions

Unit 3

MATH CORE STANDARDS I.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. I.F.IF.5 : Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. I.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. I.F.IF7 : Graph functions expressed symbolically and show key features of the graph. I.A.REI.11 : Explain why the x-coordinates of the points where the graphs y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x) I.A.CED.3 : Represent constraints by equations or inequalities and interpret solutions as viable or non-viable options in a modeling context. I.A.REI.10 : Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane. I.F.BF.1b : Write a function that describes a relationship between two quantities, combine standard function types using arithmetic operations. I.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. I.F.IF.3 : Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. Recognize arithmetic and geometric sequences as examples of linear and exponential functions. Critical Background Knowledge • Ability to graph a linear (8.F.2) or exponential function from a table or equation. • Understand the definition of a function (8.F.1) • Independent, dependent variables and input/output (8.F.1) • Graph linear functions (8.EE.5, 8.F.3, 8.F.5) • Understand that solutions to equations are values that make the equation true (6.EE.5) • Understand that a graph of a function is the set of ordered pairs consisting of an input and a corresponding output (8.F.1) • Give examples of linear equations with one solution, infinitely many solutions, or no solutions (8.EE.7a) • Reason about and solve one-variable equations and inequalities (6.EE.5 – 8) • Solve word problems leading to equations and inequalities (in one variable) (7.EE.4, 8.EE.7)

• Sole mathematical problems by graphing points in all four quadrants (6.NS.8) • Construct a function to model a relationship between two quantities (8.F.4) • Simplifying expressions (7.EE.2) • Apply integer exponent properties (8.EE.1) • Describe relationships between quantities (8.F.5) • A function is a rule that assigns to each input exactly one output (8.F.1) • Multiple representations (tables, graphs, equations, context, geometric models) (8.F.2)