What is the scope of a function

In this publication, we will consider what the scope of a function is, how it is designated and specified. We also list these areas for the most popular features.

The concept of scope

Domain is a set of values x, on which the function is defined, i.e. exists y. Sometimes called task area.

• x – independent variable (argument);
• y – dependent variable (function).

Conventional notation of a function: y=f(x).

Function is a relationship between two variables (sets). At the same time, each x matches only one specific value y.

The geometric interpretation of the domain of definition of a function is the projection of the graph corresponding to it onto the abscissa axis (0x).

Set of function values – all values yaccepted by the function on its domain. From the point of view of geometry, this is the projection of the graph onto the y-axis (0y).

The domain of definition is denoted as D (f). Instead f, respectively, a specific function is indicated, for example: D(x²), D(cos x) etc.

Then an equal sign is usually put and specific values ​​​​are written:

1. Through a semicolon, we indicate the left and right boundaries of the interval corresponding to the values ​​on the axis 0x (strictly in that order).
2. If the boundary is within the definition area, put a square bracket next to it, otherwise, a round bracket.
3. If there is no left border, we specify instead “-∞“, right – “∞“ (read as “minus/plus infinity”).
4. If necessary, if you want to combine several ranges, this is done using a special sign “∪”.

For example:

• [3; 10] is the set of all values ​​from three to ten inclusive;
• [4; 12) – from four inclusive to twelve exclusively;
• (-2; 7] – from minus two exclusively to plus seven inclusive.
• [-10; -4) ∪ (2, 8) – from minus ten inclusive to minus four exclusively and from two to eight exclusively.

Note:

• All numbers greater than zero are written like this: (0; ∞);
• All negative: (-∞; 0);
• All real numbers: (-∞; ∞) or simply R.

Domains of different functions

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General view	Function	Domain of definition (D)
Linear		With a shot	«>	Root	«>
with logarithm	Demonstration	All real numbers, with specific range dependent on value apositive or negative, integer or fractional.
Power	Just like the exponential function.
Sinus	Cosine
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