just because you know the definition of function, does that mean you understand what a function is? Explain?

Answer 1

Sure. Anybody can memorize a definition by rote. That doesn't mean they understand it.

I can memorize a saying from a foreign language, but I may not understand it at all.

Answer 2

No, just knowing the definition of a function is not enough. To understand what a function is, you need to be able to see some relations that look like functions but are not (an equation that produces a graph that is a horizontal parabola does not represent a function, for example, and you would have to know that it would fail the vertical line test, disqualifiying itself as a function.) In addition, knowing its domain and range tells you more about a particular function. There may be a change you can make to its domain (or you could misstate its domain) that would disqualify it as a function.

Answer 3

No. The definition is just the beginning of understanding. A function is a process, and there are so many different kinds of functions that I don't think the process can be explained by a definition.

Answer 4

If you understand the definition of a function, then you obviously understand what a funtion is. If you read the definition of a function, but do not have any idea what it means, then you of course you do not understand it.