Is there a difference between a non-linear equation and a function?

Question

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Answer 1

Yes, there is. They are both types of relationships, but they have slightly different requirements.

An equation just means that it is a relationship that is defined with an equals sign. So a non-linear equation just means that it has an equals sign and cannot be described in the terms of y=mx+b. Or if you haven't taken a lot of algebra, it means that the graph is a straight line that doesn't bend.

A function is any relationship of two variables that for every independant variable, normally x, there is exactly one and only one dependant variable, normally y. You can think of it as a mailbox. Every letter can go into exactly one mailbox, but each mailbox can have lots of letters.

Answer 2

Short answer: Yes.
Long answer(s):
A function is a rule that takes a value and returns exactly one value.
An equation can give you multiple values for your variables,
e.g., x^2 + y^2 = 1
or it can give you a single value; if you can solve for y, you can make an equation into a function,
e.g. y = x^2.
Furthermore, you can have a linear function, which does not correspond to any non-linear equation.

Answer 3

In mathematics, a "function" is anything where you put in one number, and get out another. Actually, you can put in several numbers, or matrices, or ... any math object, and get out several numbers, or matrices, or ... any math object.

So a function is just an input-output thing.

A non-linear equation is one type of function.