Dividing f(x) by zero. I'm currently studying calculus, and have learned some useful facts regarding operations that can be carried out on a function. For example: y = f(x) + z If we plot f(x), then plot the above, the line will be moved up on the y axis by z for every z > 0, or will be moved down by z for every z < 0 relatively to f(x) line. Similarly if I would multiply f(x) by z, the line would be moved up or down by z amount relatively to f(x) line depending if z is a negative or positive value. But is it true to state that the following cannot be defined / ploted? y = f(x) / 0 You cannot plot the above (I presume).

You cannot plot $y = f(x)/0$ since it's not even defined.