Oops, didn't see that before.

I'm not explaining very well. You said this:

Not taking "the square of a negative number" means that

**x** cannot take on negative values. Not getting "the bottom half of the "C"," to me, implies that the graph has no negative

**y** values. This is my point of contention.

The reason that the graph doesn't have a "bottom half of the "C"" is because we assume only positive values for y, as you pointed out earlier. To say that a function does not take on negative x-values means that there would be nothing to graph on the left side of the y-axis, because that's where the x-values are negative.

Let's say, for example, that we have a function defined as:

$\displaystyle y = x^2,\;\;x \ge 0$.

Then saying this would be correct:

*Remember that by the definition above we are not permitted to square a negative number, so that's why you don't get the ***left** half of the "**U**".
Hopefully that made more sense. Apologies for the confusion.

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