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How can we find the transform of a function just given its graph? I know the definition implies some type of differentiation (which should be easily obtained from the graph), but I'm still having trouble making the connection.

For example, suppose we had this graph. Is finding an explicit transform possible?enter image description here

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up vote 2 down vote accepted

Assuming you want to compute the Laplace transform (which you didn't state other than in the tags), you only have to calculate the integral

$$\mathcal{L} \left\{f(t)\right\}(s)=\int_0^{\infty} e^{-st} f(t) \,\mathrm{d}t.$$

which in your example seems to be the immediate integral

$$\mathcal{L} \left\{f(t)\right\}(s)=\int_{3}^{5} 2e^{-st} \,\mathrm{d}t.$$

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