Consider the function \(\mathrm{q}(x) = x^2\), where&nbsp;\(x\in\mathbb{R}\).
The sketch of the graph is given below:
Figure \(3\). Sketch of the graph \(y = \mathrm{q}(x) = x^2\).
<div class="content-block"><figure class="question-figure aligncenter" style="text-align: center;"><img src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1770377136351-24jktez3443.png" style="max-width: min(400px, 100%); height: auto; display: block;" alt="Figure 3: Sketch of the graph \(y = q(x) = x^2\)." class="aligncenter custom-width" /></figure></div>
When you project light rays horizontally from the points on the curve to the \(y\)-axis, you will discover that only the portion \(\{y\in\mathbb{R}:y\ge 0\}\) gets lit up. We have a neat notation \([0,\infty)\) for this subset of real numbers in interval notation:
\[R_{\mathrm{q}} = [0,\infty) := \{y\in\mathbb{R}:y\ge 0\}\]

Consider the function \(\mathrm{q}(x) = x^2\), where \(x\in\mathbb{R}\).

Figure \(3\). Sketch of the graph \(y = \mathrm{q}(x) = x^2\).

When you project light rays horizontally from the points on the curve to the \(y\)-axis, you will discover that only the portion \(\{y\in\mathbb{R}:y\ge 0\}\) gets lit up. We have a neat notation \([0,\infty)\) for this subset of real numbers in interval notation:

Functions - Range of a Function

Functions - Range of a Function