# Decreasing Function

## Decreasing Function

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 $$f\left(0\right) ≥ f\left(2\right)$$.