# How do I conveniently plot any implicit function in desmos without repetitions of code and typing?

Desmos does plot circle when I enter:

``x2+y2=1``

But when I enter:

``````f(x,y)=1

f(x,y)=x2+y2``````

It doesn't plot anything.

This problem does not exist with explicit functions, e.g. when I enter:

``````f(x)+g(x)

f(x)=x2

g(x)=x3``````

That is the same as:

``x2+x3``

Desmos does plot some cubic function.

So I can conveniently plot any explicit function without repetitions of code and typing, but not implicit functions.

Why? Does exist workaround to achieve the same goal/aim/purpose also with implicit functions too?

You can't do that because you're defining `f(x,y)` twice.

First let's understand the difference between 2 kinds of Desmos statements: Equations and Function Definitions.

These are all equations:

``````y = 1
y = x
y = x ^ 2 - x + 14
x ^ 2 + y ^ 2 = 1
x + y = 1
x / y = y / x
sin(x) = e^y
``````

They're all relationships between `x` and `y`. Desmos can and will always plot equations as long as they only use `x` and `y` as variables.

These are function definitions:

``````f(x) = x
g(x) = x ^ 2 - 2 * x + 1
D(j) = j ^ j
C(y) = e ^ y
h(x, y) = x + y - x * y
``````

They're like equations, but instead of typing `y` we give the equation a name, e.g. `f(x)` and then define it. The first 4 functions take one parameter, so they can be transformed to an equation and will be plotted:

``````f(x) = x                             //y = x
g(x) = x ^ 2 - 2 * x + 1             //y = x ^ 2 - 2 * x + 1
D(j) = j ^ j                         //y = x ^ x
C(y) = e ^ y                         //y = e ^ x
``````

However the last one takes two parameters, so it can't be plotted on the plane.

Now back to the question, try doing this:

``````f(x, y) = 1
f(x, y) = x ^ 2 + y ^ 2
f(0, 0)
``````

The last line will throw an error:

You've defined 'f' in more than one place. Try picking a different variable, or deleting some of the definitions of 'f'.

And that's exactly the issue, you defined the function `f(x, y)` in two spots, so Desmos can't tell which one to use to resolve your inquiry.

In the second example, you define `f(x)` once and `g(x)` once, and then you tell Desmos to plot the equation `f(x) + g(x)` which is basically `y = f(x) + g(x) = x ^ 2 + x ^ 3`.

Another thing is, your `f(x, y)` function takes two parameters so it'll never be plotted even if it was correctly defined once, because it's 3 dimensional but Desmos is in 2D.

For example:

``````f(x, y) = 3 x ^ 2 + x * y - 1
``````

This function will be defined successfully without throwing, but won't be plotted because it's 3 dimensional. You can only plot one 2 dimensional 'slice' of it at a time:

``````g(x) = f(x,0)
``````

This will plot.