How to plot a function which is defined on different subintervals

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I am trying to plot the function ,
But I don't know how to write the code for the definition of the function f which is given on different subintervals.

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Accepted Answer

Walter Roberson
Walter Roberson on 7 Mar 2021
There are several methods available. The most straight forward is to write a function that loops over the inputs, testing each one to decide what the result should be.
function y = f(X)
y = zeros(size(X));
for K = 1 : numel(X)
x = X(K);
if x < 2
y(K) = 0;
elseif x <= 5
y(K) = x.^2;
elseif x <= 8
y(K) = x-x.^3;
y(K) = 0;
With regards to those intervals you need, think about floor(x+1/2)
Walter Roberson
Walter Roberson on 10 Mar 2021
At asymptopic behaviour is
syms n f(x)
D = symsum(dirac(x-n), n, 1, 200)
df = diff(f)
d2f = diff(df)
eqn = d2f + D*df + f == 0
dsolve([eqn, f(0)==0])
but in practice you will not get any solution. Even if you reduce it down to dirac at one particular integer you are not going to get a solution.

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