Linear Functions Send 0 To 0

Example

The cosine function \(\cos\from \RNr\to \RNr\) is not linear because

\[\cos 0 = 1 \neq 0\]

Example

The exponential function \(\exp\from \RNr\to \RNr\), \(\exp(x)=e^x\), is not linear because

\[e^0 = 1 \neq 0\]

Example

The polynomial function \(p\from \RNr\to \RNr\), \(p(x)=2x^3 - x + 3\), is not linear because

\[p(0) = 2\cdot 0^3 - 0 + 3 = 3 \neq 0\]

Example

The function \(f\from \RNrSpc{3}\to \RNr\), \(f(x,y,z) = x + y + z -2\) is not linear because

\[f(\Vect{0}) = f(0,0,0) = 0+0+0 -2 = -2 \neq 0\]