What is the function for the number 8? [Solved!]

X

what is the function of the #8

Relevant page

<a href="/functions-and-graphs/4-graph-of-function.php">4. The Graph of a Function</a>

What I've done so far

Some trial and error, and examples on your page.

X

hello Sherry

I'm not sure whether your question means "What is the function such that when you graph it, it will give you the shape that looks like the number 8." Is that what you're trying to do?

If so, you need to use Polar Coordinates, which you can find at <a href="/plane-analytic-geometry/7-polar-coordinates.php">7. Polar Coordinates</a>.

For your problem, if you graph `r = sin theta` from `0` to `pi`, you get a circle, diameter 1 with the bottom of the circle going through the origin `(0,0)`.

Now, what you want is another circle below the original circle as you go from `pi` to `2 pi`. As a hint, the radius for the bottom circle must be positive.

Is that enough to get you started?

Good luck with it

Regards

Murray Bourne

X

Thanks.

Does `r=-sin theta` work for the bottom part?

Is it possible to do it with one function?

X

Well, `r=-sin theta` does work, but you need to specify the range of values for `theta` as part of your definition.

Can you do it with one function?

X

Is it this?

`r = sin theta` for `0 <= theta < pi`

`r = -sin theta` for `pi <= theta < 2pi`

X

Correct! It's not really a "single function", but it's probably the best we can do for this case.

We could also write it as

`r^2 = sin theta` for `0 <= theta < pi`