Difference Between Equations & Functions

[thedy]

Hi,Few days I m trying to find out,what is difference between equation and function,but as I go deeper into it,I m more confused
I give example,we have velocity as function of time:f(t)=at+Vo...Ok,so this is function of time,but why not,for example of acceleration but only time?Please try to give me some explanation or hint at least,
When I know,I have a function of time,and when of acceleration,that means,if f(t)=at+Vo,is it possible to apply this like this:f(a)=at+Vo?I assume,that is not,but why?
Thanks for every answer...

 

[AlephZero]

An equation says "something = something_else". So long as you do the same to both sides, you get another equation that means the same thing. (OK, statement is a little bit over-simplified, but let's get the basics sorted out first!)

A function looks similar, but means something different. Think of it as a "rule" that says "if you give me a value of t, this is how I find the value of f(t)."

in your example f(t)=at+Vo, you call f(t) a function of t because you are assuming the other quantities (a and Vo) are known, and t can vary. On the other hand, if t and Vo are known but the acceleration a could vary, you might want to think of it as a function of a, and write f(a) = at+Vo.

In more advanced math, often functions are often not defined by a "formula" like "at + Vo", but by a set of "rules" like

f(t) = 1 it t >= 0, and 0 if t < 0.

That's a perfectly good definition of f(t), because for any value of t you it tells you the value of f(t) (either 0 or 1). But it would be hard (and no more useful) to write a "formula" that defined the same function f(t).

 

[thedy]

An equation says "something = something_else". So long as you do the same to both sides, you get another equation that means the same thing. (OK, statement is a little bit over-simplified, but let's get the basics sorted out first!)

A function looks similar, but means something different. Think of it as a "rule" that says "if you give me a value of t, this is how I find the value of f(t)."

in your example f(t)=at+Vo, you call f(t) a function of t because you are assuming the other quantities (a and Vo) are known, and t can vary. On the other hand, if t and Vo are known but the acceleration a could vary, you might want to think of it as a function of a, and write f(a) = at+Vo.

In more advanced math, often functions are often not defined by a "formula" like "at + Vo", but by a set of "rules" like

f(t) = 1 it t >= 0, and 0 if t < 0.

That's a perfectly good definition of f(t), because for any value of t you it tells you the value of f(t) (either 0 or 1). But it would be hard (and no more useful) to write a "formula" that defined the same function f(t).

Thanks,so this is all magic?If I have other variables constant,then this,which could vary is in brackets?Like f(t),f(a)...

 

[awecrump]

Technically, a function must pass the vertical line test or that you cannot have two y values for one x value. A function usually involves two or more variables such as y=x^2+5.