Consider the function \(\mathrm{f} : \mathbb{R} \to \mathbb{R}\) defined by
\[\mathrm{f} : x \mapsto 2x + 1.\]
It is often helpful to sketch the graph of the function, namely:
\[\{(x, 2x + 1) : x \in \mathbb{R}\}.\]
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/sign/question-images/pasted/1770376568656-5sdfojq9pl.png?token=eyJraWQiOiJiZTM3ZjNhZS05OWM4LTQ5ZGQtYjRiNS1iMTBhYmJhNjY5MWYiLCJhbGciOiJIUzI1NiJ9.eyJ1cmwiOiJxdWVzdGlvbi1pbWFnZXMvcGFzdGVkLzE3NzAzNzY1Njg2NTYtNXNkZm9qcTlwbC5wbmciLCJzY29wZSI6ImRvd25sb2FkIiwiaWF0IjoxNzkzNTIwNjAwLCJleHAiOjE3OTM1MjA5MDB9.ygdUt5DRt0Hckcd3hqxouL_lnScuQk1UY9r68VMamoc" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Figure 2. Graph of \(y = f(x) = 2x+1\)." class="aligncenter custom-width" /></figure></div>
From the graph, we can see that every input \(x \in \mathbb{R}\) on the real horizontal axis yields a unique output \(y = 2x + 1 \in \mathbb{R}\).

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

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

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

Graph of linear function

Graph of linear function