Function that gives -1 and +1 with change in x.

Question

I need a function $f(x)$ that gives either $-1$ or $1$ based on $x$.

eg.

and so on.

I know it had something to do with modulas(reminders of division), but i can't get it.

x is real and i would be happy if it could change values quickly. — Yaver Javid, Aug 30 '22 at 09:00
Does it need to be continuous like $\cos(\pi x)$ or can it be disontinuous like $(-1)^{\lfloor x \rfloor}$ ? — Jaap Scherphuis, Aug 30 '22 at 09:11
@jaapScherphuis it should be continuous. values changing every 'k' change in x. ie z -> -1 , z+k -> 1, z+2k -> -1 and so on.. — Yaver Javid, Aug 30 '22 at 09:15
I don't think you know what continuous means, since the answer you just accepted is a discontinuous function. — Jaap Scherphuis, Aug 30 '22 at 09:21
sorry, im a medical student far from math. yeah i want discontinuous function. — Yaver Javid, Aug 30 '22 at 09:29

score 1 · Accepted Answer · answered Aug 30 '22 at 09:06

1

What about this one (plot)

$$f(x) = 1-2\lfloor x \rfloor+4\lfloor x/2 \rfloor$$

answered Aug 30 '22 at 09:06

user

1 Answers1