Graphs Of A Function And Its Inverse
Overview
The inverse of a function undoes it, and there is a beautiful geometric link between the two: each is the mirror image of the other in the line \(y = x\). Seeing this reflection makes inverse functions intuitive rather than abstract.
In this lesson you will use sketch graphs to show the relationship between a function and its inverse, recognising that each is the reflection of the other in the line \(y = x\).
Objectives
- Use sketch graphs to show the relationship between a function and its inverse, recognising that each is the reflection of the other in the line y = x.
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Lesson Evaluation
Congratulations on completing the lesson on Graphs Of A Function And Its Inverse. 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 function and its inverse are reflections of each other in the line: A. y = 0 B. x = 0 C. y = x D. y = -x Answer: C
- If (2, 4) lies on y = f(x), which point lies on y = f-inverse(x)? A. (2, 4) B. (4, 2) C. (-2, -4) D. (4, -2) Answer: B
- The inverse of f(x) = x^2 (x >= 0) is: A. x^2 B. 1/x^2 C. √x D. -x^2 Answer: C
- To sketch an inverse you reflect the graph in: A. the x-axis B. the y-axis C. the line y = x D. the origin Answer: C
- Reflecting (a, b) in y = x gives: A. (a, b) B. (b, a) C. (-a, b) D. (a, -b) Answer: B
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