Functions, Domain And Range
Bayani Gaba-gaba
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.
Manufura
- 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.
Takardar Darasi
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Nazarin Darasi
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- 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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