You already know how to find an asymptote, a hole, an intercept. The hard part is putting them together into one picture. So build the graph the way a mathematician actually does — one feature at a time, each one drawn the moment it is found. Pick a function, then walk the eight steps.
Pick a function
vertical asymptote end‑behavior line the curvex‑intercepty‑intercept hole
Walk a point along the curve
Drag near a dashed red wall and watch the height run away. The point traces the curve — even before the curve is drawn.
Eight steps to a finished graphchoose a function below