Drawing the graph of a function is a visual way of identifying its domain and often the most convenient way for determining its range.To figure out if a specific value is in the range of the function, we (imaginarily) draw a horizontal line passing through that specific $y$-value. If that line intersects the graph, then that $y$-value is in the range of the function. This means the horizontal projection of the graph onto the $y$-axis is the range of the function.
Similarly, to find out if a specific $x$-value is in the domain of the function, we draw a vertical line passing through that value of $x$. If this vertical line intersects the graph, then that specific value of $x$ is in the domain of the function. In other words, the domain of a function is the vertical projection of its graph onto the $x$-axis. The procedure for finding the domain and the range using the graph is shown in Figure 1.