Function Notation, Domain And Range
Overview
A function is a rule that takes each input to exactly one output, and function notation is the compact language for writing that rule down. The symbol \(f(x)\) does not mean f times x: it means the output of the function f when the input is x. This single piece of notation unlocks the whole of the functions topic.
In this lesson you will use function notation, evaluate functions, and understand the domain (the allowed inputs) and the range (the resulting outputs). You will also meet mapping diagrams, a visual way to see a function send each input to its output.
Objectives
- Use function notation, and understand the domain and range of a function, including mapping diagrams.
Audio Lesson
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Mind map
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Flashcards
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Function Notation, Domain And Range. 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) = 2x + 1, what is f(3)? A. 5 B. 6 C. 7 D. 9 Answer: C
- If f(x) = 2x + 1, what is f(-2)? A. -3 B. -1 C. 3 D. 5 Answer: A
- The set of allowed inputs of a function is its: A. range B. domain C. output D. mapping Answer: B
- What is the range of f(x) = x^2 over all real numbers? A. all real numbers B. f(x) > 0 C. f(x) >= 0 D. f(x) <= 0 Answer: C
- For f(x) = sqrt(x), the domain must satisfy: A. x > 1 B. x >= 0 C. x <= 0 D. all real x Answer: B
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