Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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### Understanding Function Iterations Every time a function is composed with itself, it is called an iteration. Iterations can be noted using a superscript. Function compositions can create iterations as well. #### Example --- #### Exercise: Your Turn! Find the first 3 iterations of \( g(x) = 3x \) if you have an initial value of 2. Fill in the table below with your answers. | Iterations | Your Work | Answer | |-----------------|-------------|--------| | \( g(2) \) | | | | \( g^2(2) \) | | | | \( g^3(2) \) | | | In this exercise, you need to apply the function \( g(x) = 3x \) iteratively starting with an initial value. #### Note: - For \( g(2) \), substitute \( x \) with 2 in the function. - For \( g^2(2) \), apply the function \( g \) to the result of \( g(2) \). - For \( g^3(2) \), apply the function \( g \) to the result of \( g^2(2) \). Write down each step of your work in the corresponding row under "Your Work", and the final result in the "Answer" column. Use this method to understand the process of function iterations and their applications.
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Transcribed Image Text:### Understanding Function Iterations Every time a function is composed with itself, it is called an iteration. Iterations can be noted using a superscript. Function compositions can create iterations as well. #### Example --- #### Exercise: Your Turn! Find the first 3 iterations of \( g(x) = 3x \) if you have an initial value of 2. Fill in the table below with your answers. | Iterations | Your Work | Answer | |-----------------|-------------|--------| | \( g(2) \) | | | | \( g^2(2) \) | | | | \( g^3(2) \) | | | In this exercise, you need to apply the function \( g(x) = 3x \) iteratively starting with an initial value. #### Note: - For \( g(2) \), substitute \( x \) with 2 in the function. - For \( g^2(2) \), apply the function \( g \) to the result of \( g(2) \). - For \( g^3(2) \), apply the function \( g \) to the result of \( g^2(2) \). Write down each step of your work in the corresponding row under "Your Work", and the final result in the "Answer" column. Use this method to understand the process of function iterations and their applications.
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