In this publication, we will consider what the range of a function is, how it is designated and specified. We also list them for common types of functions.
Content
Range definition
Range of values – set of values y, which the function accepts for all xcorresponding to its .
Note: each y matches only one specific value x.
The range of values is denoted as E(f). Its boundaries are indicated in the same way as for the domain of definitions – in round or square brackets.
For example:
- E(f) = (0; ∞).
Those. the range of the function is from zero exclusively to plus infinity, or in other words, all positive numbers.
- E(f) = (-3; 5].
Those. from minus three exclusively to five inclusive.
- E(f) = (-∞; -7) ∪ [2; ∞).
Those. from minus infinity to minus seven exclusively and from two inclusive to infinity.
Ranges of different functions
| General view | Function | Range (E) | |
| Linear | logarithmetic | Demonstration | All positive real numbers. |
| Power | Sinus | Cosine | |
| Tangent | Cotangent |