Single-variable calculus from first principles
Before you compute anything, you can learn a great deal just by reading a curve: where it lives, where it crosses, where it climbs and falls, and which invisible lines it hugs. This lesson is the vocabulary for that reading.
The domain is the set of inputs the curve is drawn over, how far left and right it goes. The range is the set of outputs it reaches, how far down and up. You read both straight off the picture: scan left-to-right for the domain, bottom-to-top for the range.
An intercept is where the curve meets an axis. The y-intercept is the height at x = 0 (where it crosses the vertical axis). The x-intercepts (also called roots or zeros) are where the curve crosses the horizontal axis, where the output is 0.