Exercise 8

Stating that a function is ‘linear’ is different than stating that its graph is a line.

• The function $f_{1}\colon\mathbb{R}\to\mathbb{R}$ given by $f_{1}(x)=2x-1$ has a graph that is a line. Show that it is not a linear function.

• The function $f_{2}\colon\mathbb{R}^{2}\to\mathbb{R}$ given by

  $$\begin{pmatrix}x\\ y\end{pmatrix}\mapsto x+2y$$

  does not have a graph that is a line. Show that it is a linear function.