Construct Linear And Exponential Functions
Overview
Two patterns of growth shape an enormous amount of the world. Linear growth adds the same amount each step, like saving a fixed sum every week. Exponential growth multiplies by the same factor each step, like money earning compound interest. Telling them apart, and writing a function for each, is a key modeling skill.
In this lesson you will construct linear and exponential functions, including arithmetic and geometric sequences, from a graph, a description or a table of values. The test is simple: a constant difference signals a linear function, a constant ratio signals an exponential one.
Objectives
- Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description or a table of values.
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Lesson Evaluation
Congratulations on completing the lesson on Construct Linear And Exponential Functions. Now that youve explored the key concepts and ideas, its time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- A constant difference between successive outputs signals which kind of function? A. linear B. exponential C. quadratic D. inverse Answer: A
- The table x = 0,1,2,3 with y = 5,8,11,14 gives the function: A. f(x) = 5x + 3 B. f(x) = 3x + 5 C. f(x) = 8x D. f(x) = 2 * 3^x Answer: B
- A constant ratio between successive outputs signals which kind of function? A. linear B. exponential C. arithmetic D. constant Answer: B
- The table x = 0,1,2,3 with y = 2,6,18,54 gives the function: A. f(x) = 2x + 4 B. f(x) = 4x + 2 C. f(x) = 2 * 3^x D. f(x) = 3 * 2^x Answer: C
- The sequence 2, 6, 18, 54 is: A. arithmetic B. geometric C. linear D. constant Answer: B
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