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 x1 and x2 of [a, b], if x1 < x2, then f(x1) ≤ f(x2).
Example
Consider the function defined by f(x) = 3x + 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) = 3x + 2 is increasing.