If \(\left[a,b\right]\) is an interval in the domain of a function \(f\), we say that the function \(f\) is decreasing in the interval \(\left[a,b\right]\) if and only if for all elements \(x_{1}\) and \(x_{2}\) of \(\left[a,b\right]\), if \(x_{1}<x_{2}\), then \(f\left( x_{1}\right) ≥ f\left(x_{2}\right)\).
Example
Consider the function defined by \(f\left(x\right) = -3x+2\).
- If \(x_{1}=0\), then \(f\left(0\right) = 2\).
- If \(x_{2}=2\), then \(f\left(2\right) = -4\).
Therefore: \(x_{1} < x_{2}\) and \(f\left(0\right) ≥ f\left(2\right)\).
