1.3 Functions and their graphs

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函数的概念已经很清楚了,这里主要学习它的英文表述。

y=f(x)y = f(x)

"y is a function of x" or "y equals f of x".

Independent variables: 自变量
Dependent variables: 应变量



严格的定义表述:"A function from a set of D to a set Y is a rule that assigns a unique (single) element f(x)Yf(x) \in Y to each element xDx \in D."

"The set D of all possible input values is called the domain of the function. The set of all values of f(x) as x varies throughout D is called the range of the function. The range may not include every element in the set Y."

"A function f have only one value f(x) for each x in its domain, so no vertical line can intersect the graph of a function more than once."



Piecewise-defined function: 分段函数

Greatest integer function or integer floor function

Least integer function or integer ceiling function