## Domain and Range on a Graphical Perspective

Two weeks ago, I  discussed the basic concepts of domain and range which I presented in an ‘algebraic way.’ In this post, I would like to discuss these concepts from a graphical perspective.

The domain of a function $x$ is the set of points on the x-axis where if a vertical line is drawn, it will hit a point on the graph. Take for instance, in the linear function $f(x) = 2x$,  we are sure that we can always hit a point wherever we draw a vertical line. In algebraic explanation, we can always find an $f(x)$ for every $x$. Therefore, we can conclude the that domain of $f$ is the set of real numbers. On the other hand, if we draw a horizontal line and it hits the graph, then it is part of the range of the graph. Clearly, the range of the $f$ is also the set of real numbers.