problems? Objective(s): Students will: Identify one-to-one functions Explore inverse functions using ordered pairs Find inverse functions using an algebraic method Graph a function and its inverse Solve applications of inverse functions Domain: Interpreting Functions Enduring Understanding(s): 4.2 Exponential Functions (Coburn) Vocabulary Cluster: Analyze functions using different 4.1 Exponential Functions (Blitzer) Exponential function, natural exponential Functions need to be understood and representations. function interpreted in terms of their context. Identify or analyze the distinguishing A function can be represented in different Additional Resource(s) properties of exponential, polynomial, ways; these different representations help Writing in Math Algebra & Trigonometry (Coburn), 2nd Edition logarithmic, trigonometric, and rational with analysis of the function. Describe the relationship between and (Exercise Videos, Lecture Videos, functions from tables, graphs, and equations. A function can be used to model the equation in logarithmic form and an equation Graphing Calculator Videos, relationship between two quantities. in exponential form. PowerPoint Presentations) New functions from existing functions can be understood and built. Explain why the logarithm of 1 with a base b Comparing linear, quadratic, logarithmic is 0. Task(s) and exponential models to solve problems is understood and applied. Explain how to find the domain of a Achieve: Spread of Disease logarithmic function. Essential Question(s): How do you evaluate exponential (Select from the tasks based upon Name some real-world examples of the use functions for given values? assessment purpose, i.e., “Developing of exponential functions. Understanding”, “Solidifying Understanding”, How do you use exponential models so or “Practice Understanding”) solve real-world problems?
problems? Objective(s): Students will: Identify one-to-one functions Explore inverse functions using ordered pairs Find inverse functions using an algebraic method Graph a function and its inverse Solve applications of inverse functions Domain: Interpreting Functions Cluster: Analyze functions using different representations. Identify or analyze the distinguishing properties of exponential, polynomial, logarithmic, trigonometric, and rational functions from tables, graphs, and equations. Enduring Understanding(s): Functions need to be understood and interpreted in terms of their context. A function can be represented in different ways; these different representations help with analysis of the function. A function can be used to model the relationship between two quantities. New functions from existing functions can be understood and built. Comparing linear, quadratic, logarithmic and exponential models to solve problems is understood and applied. Essential Question(s): How do you evaluate exponential functions for given values? How do you use exponential models so solve real-world problems? 4.2 Exponential Functions (Coburn) 4.1 Exponential Functions (Blitzer) Additional Resource(s) Algebra & Trigonometry (Coburn), 2nd Edition (Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations) Task(s) Achieve: Spread of Disease (Select from the tasks based upon assessment purpose, i.e., “Developing Understanding”, “Solidifying Understanding”, or “Practice Understanding”) Vocabulary Exponential function, natural exponential function Writing in Math Describe the relationship between and equation in logarithmic form and an equation in exponential form. Explain why the logarithm of 1 with a base b is 0. Explain how to find the domain of a logarithmic function. Name some real-world examples of the use of exponential functions.
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