Why graph a function?

Here is a simple task that will be tough without graphing: In how many points is the function

$$f(x) = x-\frac{1}{2} \left\lfloor \frac{1}{2} \left(\sqrt{8 x-7}-1\right)\right\rfloor \left(\left\lfloor \frac{1}{2} \left(\sqrt{8 x-7}-1\right)\right\rfloor +1\right)$$

not continuous? From the formula its not obvious but if you look at the graph you will see that the function does something very simple:

I suppose it would depend on the problem, or even the type of problem. In some cases, you can't just look at the equation and see what the answer could be, yet after drawing it out, you can clearly see that the line climbs for a while, then levels off at some value. $That$ value may be what you're trying to find.

Other problems you may be looking for symmetry, which you $can$ find algebraically, but it is a lot easier to just draw it and $look$ at it to see if both sides match up.