Functions, Domain And Range
Overview
Every function is a rule with two guest lists: the set of inputs it will accept, and the set of outputs it can produce. The first is the domain, the second is the range. Knowing both turns a function from a vague formula into a precisely defined object, and many of the most rewarding questions in the course hinge on getting them right.
In this lesson you will learn how to read the domain and range from a rule, why some functions need their domain restricted before they behave, and the difference between one-one and many-one functions. These ideas are the gateway to inverse and composite functions later in the syllabus.
Objectives
- Understand the terms function, domain, range (image set), one-one function and many-one function.
- Find the domain and range of functions, including composite and inverse functions.
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Lesson Evaluation
Congratulations on completing the lesson on Functions, 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.
- What is the domain of g(x) = sqrt(x - 4)? A. x >= 0 B. x >= 4 C. x <= 4 D. all real x Answer: B
- What is the range of f(x) = x^2 for all real x? A. f(x) > 0 B. f(x) >= 0 C. all real f(x) D. f(x) <= 0 Answer: B
- Which value must be excluded from the domain of h(x) = 1/x? A. x = 1 B. x = -1 C. x = 0 D. none Answer: C
- Which function is one-one over all real numbers? A. f(x) = x^2 B. f(x) = 2x + 3 C. f(x) = x^2 - 4 D. f(x) = |x| Answer: B
- For f(x) = x^2 with domain 1 <= x <= 3, what is the range? A. 0 <= f(x) <= 9 B. 1 <= f(x) <= 9 C. 1 <= f(x) <= 3 D. f(x) >= 0 Answer: B
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