A Curve-Sketching Menu (HSC SSCE Mathematics Advanced): Quizzes

A sketch shows main features, not every point

Intercepts, asymptotes, labels, scale

Simplify, use common denominator, factorise

It reveals discontinuities and asymptotes

$f(-x) = f(x)$

Point symmetry about the origin

Substitute $x = 0$ into the function

Denominator = 0 but numerator $\neq$ 0

Line $y = L$ when $f(x) \to L$ as $x \to \pm\infty$

Where curve is above or below the x-axis