This is an important page for people to understand if they want to do well later on.

I agree, your fundamentals determine your success.

Great work!

There is a mistake in spelling 1/2 way down the page: folloows -> follows, just a typing error.

The definition on the page about explicit vs implicit maybe could be more rigorous.

Def: An implicit function is a function in which the dependent variable has not been given "explicitly" in terms of the independent variable.

Is the one I like but maybe yours is better. Or maybe I didn't fully grasp yours. I don't know.

Anyway, liked the page. Thanks for the work.

]]>It would be nice for you guys to read it from top to bottom to make sure I have it all correct ... and that it reads nicely. This is an important page for people to understand if they want to do well later on.

(Link again, for reference)

]]>It is a little thing but the top the page says sqrt(x) is a function (examples of functions). While at the bottom there is a graph (vertical line test) showing that multivalued outputs (sqrt is multivalued) are not functions. Otherwise it is excellent and very functional. I kept this page for reference.

]]>Comments and suggestions welcome.

]]>Is it all good, then? Shall I link to them from my "Recent Additions" page now?

]]>I use "square root" and contrast it with √, plus I added the vertical line test and a conclusion.

Better? Any errors?

]]>Is f(x) = √x a function?

Generally speaking ... NO! ... is that a surpise?

The reason is that there could be two answers, for example f(9) = √9 = 3 or -3

This is not correct, by normal standards. Square root is a function

Square root is indeed a function for non-negative real numbers. However, it is not a function for negative real numbers or complex numbers (since, for complex numbers in general, there is no positive or negative). For example, √(−1) = ±i.

MathIsFun, you might like to add a little advanced technical stuff about the formal definition of a function: this is the usual set-theoretic definition of a function:

]]>A picture with the vertical line test would help as not many know what sin-¹ looks like.

Good idea. Plot looks like this: Plot of asin(x).

]]>