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How can I modify the equation of say $y=sin(x)$ s.t
for $x<a, y<0$,
for $a<x<b, y=sin(x)$
and for $x>b, y<0$?

Basically I want an equation to only appear on the interval $[a;b]$. In other words, shrinking down the domain to the $[a;b]$ interval by modifying the equation itself.

Csongi
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  • From a math standpoint, just define $f: [a, b] →ℝ$, with $x ↦ \sin(x)$. – flukx Apr 02 '22 at 08:54
  • It is not clear to me, what the value of the function is supposed to be for $x < a$ or $x>b$. Not defined or some specific value less than $0$. – flukx Apr 02 '22 at 08:55
  • Maybe you are looking for the "characteristic function". It is sometimes denoted by $\mathbb{1}$ or $\chi$: $\chi_A (x) = \begin{cases} 1 \text{ if } x ∈ A \ 0 \text{ if } x \not\in A \end{cases}$ Here $A$ can be any set, for example $A = [a, b]$. – flukx Apr 02 '22 at 08:56

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