Linear function

Consider the function \(\mathrm{f} : \mathbb{R} \rightarrow \mathbb{R}\) defined by

\[\mathrm{f} : x \mapsto 2x + 1\]

It is often helpful to sketch the graph of the function, namely:

\[\{(x, 2x + 1) : x \in \mathbb{R}\}\]

Using the GDC or any graphing software, we obtain:

From the graph, we can see that every input \(x \in \mathbb{R}\) on the real horizontal axis yields a unique output \(y = 2x + 1 \in \mathbb{R}\).