Functions - Range of a Function

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

The sketch of the graph is given below:

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

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

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:

\[R_{\mathrm{q}} = [0,\infty) := \{y\in\mathbb{R}:y\ge 0\}\]