[Foundations For Functions][Parameter Changes][Linear][Quad Functions][Square Root Functions][Rational Functions][Exponential & Logarithmic][Conics]
| Exponential and logarithmic Functions | |||||||
| This unit includes equations, inequalities, and systems. There should be an emphasis on the connection between the 5 representations: graph, table, problem situation, pictorial, symbolic. Within this unit, connections to foundations for functions and how all functions have same traits should be made. Make explicit connections between exponential and log functions as inverse functions. | |||||||
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| Objective | TEKS | TEKS Clarification | TAKS Objective | SATEC Lesson/Resource(s) | SATEC Correlated Assessment | Dana Center Assessments | Resources/Text |
| Use properties of exponents to simplify expressions including converting from exponential to radical form. | 2A.2A |
Revisit data activity from Foundations for Functions and reinforce common function characteristics. Revisit data to extend the investigation of Exponential and Logarithmic Functions to include writing equations, graphing and translating functions, and analyzing parameter changes in the context of situations Write exponential equations in logarithmic form and vice versa Use logarithms to solve problems involving growth and decay. Write exponential or logarithmic functions for a problem situation and determine the domain and range Numerically and algebraically develop log properties Simplify exponential equations using logarithmic properties Graph logarithmic equations using transformations Evaluate expressions and solve equations involving logarithms on the calculator Solve equations with variable exponents by using logarithms Solve Exponential inequalities Use technology such as graphing calculators and/or computers to link multiple representations |
Obj 1: Alg I A.1A, A.1B, A.1C, A.1D, A.1E Obj 2: Alg I A.2B, A.2C, A.2D, A.3A, A.3B, A.4A, A.4B Obj5: Alg I A.11A |
Solving Exponential Functions | |||
| Identify and sketch the exponential function. | 2A.4A |
Where Did the Buzz Bugs Go? Speed of a Fan |
Where
Did The Buzz Bugs Go?--Reflect and Apply Speed of Two Fans |
Algebra II Institute Part I: II. 1.1, 2 | |||
| Describe limitations of domain and range of exponential functions and examine asymptotic behavior. |
2A.11B 2A.1A |
Where Did the Buzz Bugs Go? Speed of a Fan |
Where
Did The Buzz Bugs Go?--Reflect and Apply Speed of Two Fans |
Graphing Exponential Functions | |||
| Investigate, describe and predict the effects of parameter changes on the exponential function |
2A.11B 2A.4B |
Where Did the Buzz Bugs Go? | Where Did The Buzz Bugs Go?--Reflect and Apply | Exponential Function Parameters | |||
| Develop the definition of logarithmic function as the inverse of the exponential function. |
2A.11A 2A.4C |
Comparing an Exponential Function and Its Inverse |
Intro
to Logs as inverse of Exponential Functions |
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| Identify and sketch the logarithmic function | 2A.4A | Intro to Logs as inverse of Exponential Functions | |||||
| Describe limitations of domain and range of logarithmic functions and examine asymptotic behavior. |
2A.11B 2A.1A |
Log Functions as Inverse of Exponential Functions | |||||
| Investigate, describe and predict the effects of parameter changes on the logarithmic function. |
2A.11B 2A.4B |
Transformation Two-Step Logarithmic Function Parameters |
Intro
to Logs as inverse of Exponential Functions Graphs of Log Functions Algebra II Institute Part 1: 1.1, 2.1 |
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| Solve exponential and logarithmic equations using graphs, tables, and algebraic methods. |
2A.11A 2A.2A |
Where Did the Buzz Bugs Go? Speed of a Fan |
Where
Did The Buzz Bugs Go?--Reflect and Apply Speed of Two Fans |
Bighorn Sheep |
Intro
to Logs as inverse of Exponential Functions Solving Log Equations Algebra II Institute Part I: II. 2.1 |
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| Determine reasonableness of solutions to exponential and logarithmic equations | 2A.11C | Speed of a Fan | Speed of Two Fans | ||||
| Analyze a situation modeled by an exponential function, formulate an equation or inequality, and solve the problem using graphs, tables, and algebra |
2A.11F 2A.11D |
Where Did the Buzz Bugs Go? Speed of a Fan |
Where
Did The Buzz Bugs Go?--Reflect and Apply Speed of Two Fans |
Saving Money, Making Money | Algebra II Institute Part I: II. 2.1 | ||
| Collect and organize data , make scatterplots, fit the curve to a function, interpret the results, and model, predict, and make decisions. | 2A.1B |
Where Did the Buzz Bugs Go? Speed of a Fan |
Where
Did The Buzz Bugs Go?--Reflect and Apply Speed of Two Fans |
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| Recognize that functions can be denoted in many forms: y =, d =, y = and f(x) = and determine which form is the most appropriate for a given situation | A.4C | ||||||
| Students perceive functions and equations as means for analyzing and understanding relationships and as a tool for expressing generalizations. | BU A3 | ||||||
| Students use a variety of representations, tools, and technology and model situations to solve problems. | BU A5 |
Where Did the Buzz Bugs Go? Speed of a Fan |
Where
Did The Buzz Bugs Go?--Reflect and Apply Speed of Two Fans |
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| Use math processes throughout, including problem solving, computation, communication, connections, reasoning, multiple representations, modeling, and justification | BU A6 |
Where Did the Buzz Bugs Go? Speed of a Fan |
Where
Did The Buzz Bugs Go?--Reflect and Apply Speed of Two Fans |
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