Graphing Calculator

What a "gap" in the graph usually means

If a function fails to plot at certain x-values — like 1/x at x = 0, or √x for negative x — that's not a rendering bug. It means the function is genuinely undefined there, and the graph correctly shows a gap or asymptote instead of a continuous line.

Reading the shape, not just the plot

Zooming too far in or out can make a smooth curve look like a straight line, or make an asymptote appear to touch an axis it never actually reaches. Adjust the view window deliberately when a function's behavior near zero or infinity is what you're trying to understand.