Obtaining the range of a given function from its graph

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

The sketch of the graph is given below:

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:

\[R_q = [0, \infty) := \{y \in \mathbb{R} : y \ge 0\}.\]