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Mathematics · Glossary

What is Reference functions?

Also known as: hyperbola

Definition 11.3 High School Mathematics · Chapter 11 — Functions and Variations
x↦x2 (square),x↦x3 (cube),x↦x,x↦1x,x↦∣x∣.x \mapsto x^2 \text{ (square)}, \quad x \mapsto x^3 \text{ (cube)}, \quad x \mapsto \sqrt{x}, \quad x \mapsto \frac{1}{x}, \quad x \mapsto \abs{x}.

Their domains are R\R, R\R, [0, +∞)\intco{0}{+\infty}, R∖{0}\R \setminus \{0\} and R\R respectively. The curve of x↦1xx \mapsto \frac1x is a hyperbola.

The five reference curves: the parabola x2 and the cube x3 (left); √ x, x and the hyperbola 1x (right). The five reference curves: the parabola x2 and the cube x3 (left); √ x, x and the hyperbola 1x (right).
The five reference curves: the parabola x2x^2 and the cube x3x^3 (left); x\sqrt x, ∣x∣\abs x and the hyperbola 1x\frac1x (right).
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