Curve sketching

Curve sketching is a way of interpreting a given equation as a diagram. More specifically, this allows students to visually represent limit behaviours in a way that follows university mathematics. In the HSC, curve sketching is predominantly an Extension 2 topic. However, basic graphs can often be asked in Extension 1.

Systematic approach

Graphing ${\frac {1}{f(x)}}$

1995 3a (iv)

${\text{Let }}f(x)=-x^{2}+6x-8.$

${\text{On separate diagrams, and without using calculus, sketch the following graphs.}}$ ${\displaystyle }$ ${\text{Indicate clearly any asymptotes and intercepts with the axes.}}$ ${\displaystyle }$