# What does Overlap two functions mean

What does overlap mean in the case of two functions. Or atleast, what does overlap mean in the case of 2 lines or 2 curves.

The complete sentence to clarify the context:

Convolution is a mathematical operation that takes two functions and measures their overlap. To be more specific, it measures the amount of overlap as you slide one function over another. For example, if two functions have zero overlap, the value of their convolution will be equal to zero. If they overlap completely, their convolution will be equal to one. As we slide between these two extreme cases, the convolution will take on values between zero and one.

• It can mean different things depending on the precise context. Could you please post (i) the complete sentence that contains the word; and (ii) the source of that sentence? Feb 23, 2012 at 17:46
• I edited the questions. Thanks for the response. Feb 23, 2012 at 18:40
• Did you try this? Feb 23, 2012 at 19:17
• That link is not much help because I am trying to understand what does overlap mean in this context. Feb 23, 2012 at 19:20

If you imagine a function as corresponding to its graph on the plane, you can take two functions, $f$ and $g$, graph them on separate transparent sheets of plastic, and then place the two sheets one on top of the other; "overlap" would refer to the section of the plane that lies simultaneously between the $X$-axis and the graph of $f$, and between the $X$-axis and the graph of $g$.