Maths AA terms: O

O

Oblique asymptoteHL only · also slant asymptote

A straight line $y = mx + c$ with $m \neq 0$ that a graph approaches as $x \to \pm\infty$. A rational function whose numerator has degree exactly one more than its denominator has one, found by polynomial division.

Introduced in 2.13 Rational functions

Odd functionHL only

A function for which $f(-x) = -f(x)$ for every $x$ in its domain. Its graph has rotational symmetry of order 2 about the origin, for example $y = x^3$

Odd numberalso odd integer

An integer that leaves remainder $1$ when divided by $2$, so it can be written as $2n + 1$ for some integer $n$. Examples are $-3$, $1$

One-sided limitHL only · also left-hand limit, right-hand limit

The value $f(x)$ approaches as $x$ tends to $a$ from one side only: $\lim_{x \to a^-} f(x)$

One-to-one functionalso injective

A function in which different inputs always give different outputs, so each output comes from exactly one input. Its graph passes the horizontal line test.

Introduced in 2.2 Functions, domain, range and inverse

Optimisationalso optimization

Finding the greatest or least value of a quantity, such as an area, a cost or a time, by writing it as a function of one variable and locating its maximum or minimum on the allowed domain.

Introduced in 5.8 Stationary points, optimisation and inflexion

Order of magnitudealso orders of magnitude

The power of 10 that a quantity is closest to, given by $k$ when it is written as $a \times 10^k$. Two quantities differ by one order of magnitude when one is about 10 times the other.

Introduced in 1.1 Scientific notation

Outcomealso possible outcome

One possible result of a trial. Exactly one outcome occurs each time the trial is carried out.

Introduced in 4.5 Concepts of probability

Outer function

In a composite function $f(g(x))$, the function $f$ that is applied last, to the output of the inner function $g$. In $\sin(x^2)$

Outlieralso outliers

A data value that lies unusually far from the rest of the data. A value is treated as an outlier when it is more than $1.5 \times \mathrm{IQR}$ below $Q_1$ or above $Q_3$