How Do You Creat A Moving Mental Image From An Equation?

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When you read an equation, how are you able to then take the bits of that equation and translate it into a mental picture that allows you to visualize what the particular equation is describing?
 
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It helps to be familiar with basic functions commonly found in math (and physics, for that matter): sine, cosine, exponential, polynomial, reciprocal, etc. You can form a mental picture if you have already seen a particular class of function many times before.

If a function is some complicated mixture of other functions, one may just have to create an actual graph rather than trying to visualize it mentally.
 
graph it
 
What an equation "describes" depends upon the application, not the equation. Exactly the same equation may describe many different situations. If you mean "given an equation, determine some some situation that it might describe", perhaps to give you some ideas on how to simplify the equation or do something else with it, that comes with having done lots and lots of appliations.
 

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