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Edexcel IGCSE Maths 复习笔记 3.2.4 Functions - Domain, Range & Exclusions

Category: IGCSE课程, 国际课程, 教材笔记, 福利干货 Date: 2022年6月28日下午2:51

Edexcel IGCSE Maths 复习笔记 3.2.4 Functions - Domain, Range & Exclusions

Functions are a formal way of writing mathematical expressions
- eg. f(x) = 3x + 2 would be a linear function
- eg2. g : x ⟼ x² + 3x – 5 would be a quadratic function

3.2.4-DRE-Notes-fig1

The domain of a function is the values of x (the “input”) are allowed to take
For some functions, x cannot be certain values
- eg. f(x) = 1 / xx cannot take the value 0
Other times we may choose to restrict the values of x
- eg. The function g(x) = 5 – 2x² is used to model the height of water throughout the day where x indicates timeIt may make sense to limit x so it only covers a 24 hour period
Inequalities are used to describe the values x can take
Any exclusions are usually indicated using the “not equal to” symbol (≠)

3.2.4-DRE-Notes-fig2

The range of a function is the values of f (the “output”) that could occur
Some functions can never take certain values, regardless of the value of x
- eg. f(x) = x²f, a squared (real) value, cannot be negative
- eg2. g(x) = 1 / xg can never be zero (because numerator cannot be 0)
The range of a function can be influenced by its domain
As with the domain, inequalities are used to describe the values a function can take and “not equal to” (≠) is used for any exclusions

3.2.4-DRE-Notes-fig3

3.2.4-DRE-Notes-fig4

You need to be able to identify and explain any exclusions in the domain of a function
You need to be able to deduce the range of a function from its expression and domain
You may also be asked to sketch a graph of a function
- This could involve sketching parts of familiar graphs that are restricted because of the domain and exclusions

3.2.4-DRE-Notes-fig5

Make sure you are familiar with inverse functions, denoted by f^-1, g^-1, etc.
The range of a function is the domain of the inverse function
The domain of a function is the range of the inverse function