# What is an affine function?

Consider a functional, what is meant by a minimal sequence consistent of 'piecewise affine functions'?

• $f$ is affine function, if $x\mapsto f(x)-f(0)$ is linear. – Berci Nov 2 '12 at 11:55
• Could you give some context? – martini Nov 2 '12 at 12:10
• I want to show that an minimum of an energy-functional does not exist. – AlexisZorbas Nov 2 '12 at 13:02
• Is arctan an affine function? – AlexisZorbas Nov 2 '12 at 15:08
• @AlexisZorbas Affine functions are those of the form $f(x)=ax+b$ for some constants $a$ and $b$. Of course, $\arctan$ is not of that form. – Mohsen Shahriari Jun 12 '15 at 9:17