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.
Objective(s): Students will: Evaluate an exponential function Graph general exponential functions Graph base-e exponential functions Solve exponential equations and applications Domain: N-NE – Number Expressions Cluster: Represent, intercept, compare, and simplify number expressions. 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 use transformations to sketch graphs of exponential and logarithmic functions? How do you solve exponential and logarithmic equations? Objective(s): Students will: 4.3 Logarithms and Logarithmic Functions (Coburn) 4.2 Logarithmic Functions (Blitzer) Additional Resource(s) Algebra & Trigonometry (Coburn), 2nd Edition (Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations) Task(s) Select from the following tasks: What is a Logarithm? p. 40 Evaluating Logarithms that are not Common or Natural .p. 51 The Logarithmic Function p. 57 How Long Does It Take? p.64 Zombies Revisited – Can You Model Zombie Growth? p.72 Half-Life p.78 How Does Your Money Grow? p. 86 Applications of Logarithmic Functions p. 99 Newton’s Law of Cooling-Coffee, Donuts, and (later) Corpses p. 107 Vocabulary Transcendental function, logarithmic function, common logarithm, natural logarithm Writing in Math Compare and contrast exponential functions and logarithmic functions. Describe the product rule for logarithms and give an example. Describe the quotient rule for logarithms and give an example. Describe the power rule for logarithms and give an example. You overhear a student talking about a property of logarithms in which division becomes subtraction. Explain what the student means by this.
half-angle identities Derive and use the product-to-sum and sum-to-product identities Solve applications using these identities GSE Pre-Calculus: Unit 4 Trigonometric Identities Double-Angle Identities for Sine, Cosine, and Tangent p. 38 The Cosine Double-Angle: A Man with Many Identities p. 43 The power-reducing formula for the sine squared of an angle The power-reducing formula for the cosine squared of an angle Domain: Building Functions Cluster: Build new functions from existing functions. Find inverse functions (including exponential and logarithmic) Enduring Understanding(s); Exponential and logarithmic functions are inverse functions. Mathematical functions can be used to solve real world applications. Essential Question(s) How can graphs and equations of functions and their inverses help us to interpret real world problems? How can analytic and graphical methods be used to support each other in the solution of a problem? Objective(s): Students will: Find and graph the inverse sine function and evaluate related expressions Find and graph the inverse cosine and tangent functions and evaluate related expressions Apply the definition and notation of inverse trig functions to simplify compositions 6.5 Inverse Trigonometric Functions and their Applications (Coburn) 5.7 Inverse Trigonometric Functions (Blitzer) Additional Resource(s) Algebra & Trigonometry (Coburn), 2nd Edition (Exercise Videos, Lecture Videos, Graphing Calculator Videos, PowerPoint Presentations) Task(s) Inverse Trigonometric Functions (p.31) Vocabulary Inverse functions Writing in Math Explain why, without restrictions, no trigonometric function has an inverse. How can the graph od y = sin-1x be obtained from the graph of the restricted sine function? Describe the restriction on the sine function so that it has an inverse function. Describe the restriction on the cosine function so that it has an inverse function.
RESOURCE TOOLBOX Textbook Resources Standards (formerly tncore.org) TN Advanced Algebra & Trigonometry Standards ) Videos Calculator Interactive Manipulatives http://www.mathopenref.com Edugoodies Additional Sites Literacy ACT Tasks/Lessons