A function that is naturally periodic?

**ruthvik** · February 24th 2009, 12:42 PM

ok guys, im having trouble with this problem
this is due very soon

this was the question given

Identify a function that is naturally periodic (not a horizontal line or one that involves trig functions).

Identify the period.

Graph the function.

what does it mean by naturally periodic? maybe i can do it if i know what it means, also how do i figure out a period of a regular function? i only know how to do it to trig functions

any help is appreciated, thanks

**Plato** · February 24th 2009, 01:01 PM

Originally Posted by ruthvik

Identify a function that is naturally periodic (not a horizontal line or one that involves trig functions).

Use the floor function: $f(x) = x - \left\lfloor x \right\rfloor$

**sinewave85** · February 24th 2009, 01:05 PM

Originally Posted by ruthvik

ok guys, im having trouble with this problem
this is due very soon

this was the question given

Identify a function that is naturally periodic (not a horizontal line or one that involves trig functions).

Identify the period.

Graph the function.

what does it mean by naturally periodic? maybe i can do it if i know what it means, also how do i figure out a period of a regular function? i only know how to do it to trig functions

any help is appreciated, thanks

A function that is naturally periodic is any function based on a cyclical variable. One good "natural" cyclical variable is clock time. You can set up a simple equation with time as the variable, like y = 2t, and they graph the equation with t as the horizontal axis.

**ruthvik** · February 24th 2009, 01:08 PM

Originally Posted by sinewave85

A function that is naturally periodic is any function based on a cyclical variable. One good "natural" cyclical variable is clock time. You can set up a simple equation with time as the variable, like y = 2t, and they graph the equation with t as the horizontal axis.

i dont understand what cyclical variables are

also, i dont know what that equation the other guy made, i can graph it but im thinking of this answer in more simple terms

**sinewave85** · February 24th 2009, 01:27 PM

Originally Posted by ruthvik

i dont understand what cyclical variables are

also, i dont know what that equation the other guy made, i can graph it but im thinking of this answer in more simple terms

Sorry, the answer I gave won't work because it it not a function -- it wont pass the vertical line test. I am trying to think of a way to construct a simple periodic function -- one the oscillates up and down -- without using a sin function.

**Plato** · February 24th 2009, 01:49 PM

What do you not like about my function? It has a natural period of 1.

**ruthvik** · February 24th 2009, 01:52 PM

Originally Posted by Plato

What do you not like about my function? It has a natural period of 1.

i never learned that function, so i cannot use it, otherwise i would have : D

thanks though

**Plato** · February 24th 2009, 01:57 PM

Originally Posted by ruthvik

i never learned that function, so i cannot use it, otherwise i would have.

You mean that you never learned the greatest integer function?
The floor function is just a more modern notation for that.

**ruthvik** · February 24th 2009, 02:14 PM

Originally Posted by Plato

You mean that you never learned the greatest integer function?
The floor function is just a more modern notation for that.

oh wow?? really? i learned GINT, but tell me plato, if my teacher asks how i got this, how will i explain to him? how can i graph this on paper? because i only learned what it is , will it work if i use plug in for x and stuff?

**Plato** · February 24th 2009, 02:28 PM

For every x, $\left\lfloor x \right\rfloor \leqslant x < \left\lfloor x \right\rfloor + 1\; \Rightarrow \;0 \leqslant x - \left\lfloor x \right\rfloor < 1$ .

As you can see the graph goes from 0 to 1 (never equal to 1) between any two consecutive integers.

**ruthvik** · February 24th 2009, 03:39 PM

Originally Posted by Plato

For every x, $\left\lfloor x \right\rfloor \leqslant x < \left\lfloor x \right\rfloor + 1\; \Rightarrow \;0 \leqslant x - \left\lfloor x \right\rfloor < 1$ .

As you can see the graph goes from 0 to 1 (never equal to 1) between any two consecutive integers.

this might be a stupid question but when i graph it, there is a open circle on the top part right? like (1,1)

thanks btw, your eq was a good example

**Plato** · February 24th 2009, 03:51 PM

Originally Posted by ruthvik

this might be a stupid question but when i graph it, there is a open circle on the top part right? like (1,1)

thanks btw, your eq was a good example

yes

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