What the app does
The plot is assembled from everything above: asymptotes as dashed guides, turning points and inflections as marked dots, and the curve itself cut into separate branches wherever it leaves the domain or jumps a pole, so two sides of an asymptote are never joined by a line that does not exist.
Why it matters
Drawing the curve is the check on the other nine steps. If the sketch does not match the signs, limits and turning points you worked out, one of them is wrong — and finding out which is where the understanding happens.
Read further
- Graph of a function Wikipedia
- Curve sketching Wikipedia
- Derivatives and the shape of a graph OpenStax Calculus