Topic: summing functions with different arguement ranges

I would like to graph a series of functions, each with a different argument range, and then show the summation of these functions.

In particular, each of the functions is concave downward and crosses the x axis at two points (like a 1-x^2 curve), and in each case, only the non-negative part is physically meaningful.

Is there a way to specify that the argument range of function F1 is AR1 (chosen so that negative values don't occur), the argument range of F2 is AR2 (likewise), but plot F1+F2 without limiting the argument range?

In other words, I want to add all non-negative values of F1 to all non-negative values of F2 and plot that.

Can anyone help? Many thanks.

john

  • pin
  • Member
  • Offline

Re: summing functions with different arguement ranges

You can use the unit step function u(z) twice to zero a function for arguments below x1 and over x2:
f(x) = u(x-x1) * F(x) * u(x2-x).

Try to plot your function:
f(x) = u(x+1) * (1 - x^2) * u(1-x)

See Help for details to u(z) function.

Re: summing functions with different arguement ranges

As an alternative to the unit step, where you specify the x-coordinate as limit, you can use the max function like this:
f(x)=max(0, 1 - x^2)

This will ensure that the values are never less than 0.