If [

*a*,

*b*] is an interval in the domain of a function

*f*, we say that the function

*f* is increasing in the interval [

*a*,

*b*] if and only if for all elements

*x*_{1} and

*x*_{2} of [

*a*,

*b*], if

*x*_{1} <

*x*_{2}, then

*f*(

*x*_{1}) ≤

*f*(

*x*_{2}).

### Example

Consider the function defined by *f*(*x*) = 3*x* + 2.

- If \(x_{1} = 0\), then
*f*(0) = 2.
- If \(x_{2} = 2\), then
*f*(2) = 8.
- Therefore:
* f*(0) ≤ *f*(2).
- And the function defined by
*f*(*x*) = 3*x* + 2 is increasing.