Is this a graph of a delta function?

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SUMMARY

The discussion centers on sketching the delta function g(x) = δ(y+a) + δ(y) + δ(y-a). Participants clarify that the delta function is not a conventional function but rather a distribution that cannot be plotted in the traditional sense. The delta function is characterized by its property that the integral of δ(x)f(x)dx equals f(0). The consensus is that while the delta function cannot be graphically represented as a true function, it can be conceptually visualized as infinitely high vertical lines at the specified points -a, 0, and a.

PREREQUISITES
  • Understanding of delta functions in mathematical analysis
  • Familiarity with the properties of distributions
  • Knowledge of integration and its applications in physics
  • Basic concepts of precalculus and graphing functions
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Students and educators in mathematics and physics, particularly those studying advanced calculus or mathematical analysis, will benefit from this discussion on the delta function and its properties.

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Homework Statement


My question asks me to sketch the following:
g(x) = \delta (y+a) + \delta (y) + \delta (y-a)


Homework Equations





The Attempt at a Solution


delta.jpg


I think this is it, but am I correct? I don't recall actually seeing a delta function other than a Kronicker(sp?) delta function, and I'm pretty sure that this isn't one of that type. Research on the web therefore leads me to this (because after trawling my notes I can't actually find anything about it in the entire course!).
 
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another delta function is such a function that integral of d(x)f(x)dx is f(0), and defined like this it can't really be plotted.
 
Well, except that those aren't infinitely tall! Actually, I don't think that is a very good question because the "delta function" isn't a true "function" and doesn't have a graph. A rough "physicist's" idea of the graph of a delta function \delta(x) would be an infinitely high vertical line at x= 0. Since this is in "precalculus", your three (infinitely high) vertical lines at -a, 0, and a are what I would guess are intended here.
 

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