Reciprocal functions (HSC SSCE Mathematics Extension 1): Flashcards

A reciprocal function is $y = \frac{1}{f(x)}$.

They occur where the function is undefined, not zero.

It's the line $y = k$ that $f(x)$ approaches as $x \to \pm \infty$.

Set the denominator to zero; solve for x values.

$\frac{1}{f(x)} \to 0$ indicates a horizontal asymptote.

Reflect the graph across the line $y = 1$ and invert values.

Points where $f(x) = 1$ or $f(x) = -1$ match these.

Intersections occur where $f(x) = g(x)$.

Look for symmetry around vertical asymptotes and lines.

It visualizes complex behaviors like symmetry and intersections.