Well, it sounds like a plausible statement, and maybe it would be true . But we have
no idea what the graph of two functions is.
Perhaps you could graph the sum of two functions, or the difference of two functions,
or their product, or their quotient. We believe that if the original two functions are
both continuous, then their sum and difference would also be continuous, but their
product and their quotient might not necessarily be continuous. However, we still
don't know what the "graph of two functions" is.
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The graph of a continuous function will not have any 'breaks' or 'gaps' in it. You can draw it without lifting your pencil or pen. The graph of a discrete function will just be a set of lines.
continuous
If you are looking at a graph and you want to know if a function is continuous, ask yourself this simple question: Can I trace the graph without lifting my pencil? If the answer is yes, then the function is continuous. That is, there should be no "jumps", "holes", or "asymptotes".
It can be continuous or discrete.
A continuous linear function produces a straight line graph that can be extended indefinitely in either direction. If the two ordered pairs are plotted on a graph then a straight line can be drawn joining these points. If that line is extended beyond both ends then there are no set limits and the function becomes continuous.