HSC Extension 1 and 2 Mathematics/4-Unit/Graphs

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.

Introduction

Systematic approach

Domain and range

Asymptotes

Horizontal asymptotes

Oblique asymptotes

Vertical asymptotes

Limit behaviours

Intercepts

Graphing $f^{-1}(x)$

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

1995 3a (iv)

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

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

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