Modulus Functions
Overview
The modulus (or absolute value) of a number is its size, ignoring sign, so it is never negative. Applying the modulus to a function flips any negative part of its graph above the x-axis, producing the distinctive 'bounce' you see in modulus graphs.
In this lesson you will understand the relationship between the graph of \(y = f(x)\) and the graph of \(y = |f(x)|\), where \(f(x)\) may be linear, quadratic, cubic or trigonometric.
Objectives
- Understand the relationship between the graph of y = f(x) and the graph of y = |f(x)|, where f(x) may be linear, quadratic, cubic or trigonometric.
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Flashcards
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Modulus 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.
- The graph of y = |f(x)| is obtained from y = f(x) by: A. reflecting in the y-axis B. reflecting the part below the x-axis up C. shifting up D. rotating Answer: B
- What is the value of |{-7}|? A. -7 B. 0 C. 7 D. 49 Answer: C
- The graph of y = |x - 2| has its lowest point at: A. (0, 2) B. (2, 0) C. (-2, 0) D. (0, -2) Answer: B
- y = |f(x)| can never be: A. zero B. positive C. negative D. large Answer: C
- For x < 2, y = |x - 2| equals: A. x - 2 B. 2 - x C. x + 2 D. 0 Answer: B
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