High School Math Guide

Linear and Exponential Functions

Unit 2

MATH CORE STANDARDS 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. I.F.BF.1 : Write a function that describes a relationship between two quantities. I.F.LE.1 : Distinguish between situations that can be modeled with linear functions and with exponential functions. I.F.LE.2 : Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs. I.F.LE.3 : observe using graphs and table that a quantity increasing exponentially eventually exceeds a quantity increasing linearly. I.F.LE.5 : Interpret the parameters in a linear or exponential function in terms of a context. I.F.IF.7 : Graph functions expressed symbolically and show key features of the graph. I.F.BF.2 : Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. I.A.SSE.1 : Interpret expressions that represent a quantity in terms of its context. I.A.CED.2 : Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. I.F.IF.6 : Calculate and interpret the average rate of change of a function.

Critical Background Knowledge

• Understand the definition of a function (8.F.1, 8.F.3) • Simplifying expressions (7.EE.2) • Apply integer exponent properties (8.EE.1) • Construct linear functions (8.F.4) • Describe relationships between quantities (8.F.5)

• Describe where a function is increasing or decreasing (8.F.5) • Identify the constant rate of change (7.RP.2b, 8.EE.5, 8.F.4, 8.F.5) • Construct a function to model linear situation (8.F.4) • Perform operations using whole number exponents (6.EE.2c) • Identify, compare, and interpret rates of change (7.RP.2b, 8.F.2, 8.EE.5) • Identify linear and nonlinear functions from a graph or a table (8.F.4, 8.F.5)

• Compare proportional relationships y = mx to other linear relationships y = mx + b (7.RP.2, 8.F.3, 8.EE.5) • Compare properties of two functions, interpret the equation y = mx + b , and interpret the rate of change and initial value (8.F.2, 8.F.3, 8.F.4) • Graph linear functions (8.EE.5, 8.F.3, and 8.F.5)

• Understand that rewriting an expression can highlight quantities (7.EE.2) • Determine rate of change and initial value of a function (8.F.3, 8.F.4) Continued on next page