IB Maths AA 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 highest power of $x$ with a non-zero coefficient in a polynomial.

A polynomial expression that divides another polynomial exactly, leaving remainder $0$.

The statement that $f(a)=0$ if and only if $(x-a)$ is a factor of $f(x)$.

Functions that can be written as a quotient of two polynomials, for example $f(x)=\frac{ax+b}{cx^2+dx+e}$, with a domain excluding values that make the denominator $0$.

When a polynomial $f(x)$ is divided by $(x-a)$, the remainder is $f(a)$.

A value $a$ such that $f(a)=0$ for a given function or polynomial; corresponds to an $x$-intercept of the graph.