Functions And Notation
Overview
A function is a rule for turning one number into another, and once you can name that rule you can start combining rules, reversing them, and asking exactly which inputs are allowed. This topic gives you the notation that makes all of that precise: f(x), f: x → ..., domain, range, composite functions and inverse functions.
These ideas sit underneath almost everything else in the specification, from graph sketching to calculus, so getting the notation fluent now pays off across the whole course.
Objectives
- Understand the idea of a function of a variable
- Understand a function as a mapping or as a correspondence between the elements of two sets
- Use functional notations of the form f(x) = ... and f: x -> ...
- Understand and use domain and range of a function
- Find and use composite functions
- Find and use inverse functions
Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Functions And Notation. 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.
- If f(x) = 3x - 5, what is f(4)? A) 7 B) 12 C) 17 D) -7 Answer: A
- If f(x) = x^2 + 1 and g(x) = x - 2, what is fg(3)? A) 2 B) 7 C) 8 D) 10 Answer: A
- Which value must be excluded from the domain of h(x) = 1/(x - 6)? A) x = 0 B) x = -6 C) x = 6 D) x = 1 Answer: C
- If f(x) = 5x + 2, what is f^-1(x)? A) (x - 2)/5 B) (x + 2)/5 C) 5x - 2 D) x/5 - 2 Answer: A
- A function that has an inverse must be: A) many-to-one B) one-to-one C) always increasing D) always positive Answer: B
Available on the Green Bridge App
Download the Green Bridge CBT app on your phone or computer to access full lesson notes, practice questions, and more.
Available on the Green Bridge App
Download the Green Bridge CBT app on your phone or computer to access full lesson notes, practice questions, and more.
Recommended Books
Practice Mock Questions
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