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.

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.}$$ $$$$