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I really don't know how to we say that a log function would look like this or polynomial function would look like this. I know that if I have like $X + Y = c$, I can draw straight line by taking values of $X$ and evaluating $Y$.

How to I learn graph plots for other math function (log, exponential, sine, cos etc.) or polynomials of degree $n$?

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    Calculus + Memorization. If you know a handful of graphs like $y=\ln(x)$, $y=e^x$, $y=\sin(x)$, lines, and parabolas and also use $f'(x)$ to tell when the function is increasing or decreasing and $f''(x)$ to tell if it's concave up or down you can sketch graphs of a lot of things.2011-10-30
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    you can know how a graph of a function looks, by drawing it using a computer program (graphic calculator). you can use this one for example: http://javaboutique.internet.com/PGC/2011-10-30
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    http://peda.com/grafeq/2011-10-31

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