IB Maths AI 2.5 Definitions

Lines that a rational function’s graph approaches; can be vertical where the denominator is $0$ (and the numerator is not $0$ there), horizontal depending on degrees, or oblique when the numerator’s degree is one more than the denominator’s.

The set of input values for which a model is intended to be used, chosen using the context rather than only the algebraic definition.

A rule that takes each input and gives exactly one output; used to model relationships between quantities, such as velocity as a function of time.

A way to name the output of a function for a given input, for example writing $f(x)$ to mean the output of the function $f$ when the input is $x$.

A function that returns the input unchanged, given by $I(x)=x$; composing a function with its inverse gives this function.

A function that reverses the effect of another function, so that if $f$ maps $x$ to $y$ then $f^{-1}$ maps $y$ back to $x$, with $\left(f\left(f^{-1}(x)\right)\right)=x$ and $\left(f^{-1}\left(f(x)\right)\right)=x$ when both are defined.

A function of the form $f(x)=ax^2+bx+c$ whose graph is a parabola, with $y$-intercept $(0,c)$ and axis of symmetry $x=\frac{-b}{2a}$.

The set of possible outputs a function can produce.