Question

Опишите свойства функции y = f(x)

Answer 1

Определение : Числовой функцией называется соответствие, которое каждому числу х из некоторого заданного множества сопоставляет единственное число y.Обозначение:y = f(x),где x – независимая переменная (аргумент), y – зависимая переменная (функция). Множество значений x называется областью определения функции (обозначается D(f)). Множество значений y называется областью значений функции (обозначается E(f)). Графиком функции называется множество точек плоскости с координатами (x, f(x))

Answer 2

Properties of the Function y = f(x)

The function y = f(x) represents a relationship between the independent variable x and the dependent variable y. Let's explore some general properties of this function.

1. Function Representation: The function y = f(x) can be represented in various forms, such as algebraic expressions, graphs, or tables, to illustrate the relationship between x and y.

2. Domain and Range: - The domain of the function y = f(x) is the set of all possible input values of x for which the function is defined. - The range of the function y = f(x) is the set of all possible output values of y that the function can produce.

3. Transformations: - The function y = f(x) can undergo transformations such as translations, reflections, stretches, and compressions, which alter its graph and equation.

4. Inverse Function: - The inverse function of y = f(x), denoted as y = f^(-1)(x), represents the reverse relationship, where the roles of x and y are interchanged.

5. Special Function Forms: - The function y = f(x) can take various specific forms, such as square root functions, logarithmic functions, trigonometric functions, rational functions, and absolute value functions.

6. Mathematical Operations: - Mathematical operations like addition, subtraction, multiplication, division, composition, and differentiation can be performed on the function y = f(x) to create new functions or analyze its properties.

These properties provide a general understanding of the function y = f(x) and its behavior in mathematical contexts.