IB Maths AA 2.7 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.

A function rule that assigns each input $x$ a single output value, written as $f(x)$.

The multiplicative inverse of a non-zero number, so multiplying a value by its reciprocal gives $1$ (for example, the reciprocal of $a$ is $\frac{1}{a}$).

Formed by keeping the parts of $y=f(x)$ that are on or above the $x$-axis unchanged and reflecting any parts below the $x$-axis in the $x$-axis, so all outputs are non-negative.

Formed by taking the part of $y=f(x)$ for $x\geq0$ and reflecting it in the $y$-axis to create the part for $x\lt0$, giving a graph symmetric about the $y$-axis.

A horizontal transformation determined by the expression inside the function: the factor $a$ produces a horizontal stretch or compression and the constant $b$ produces a horizontal shift, often clarified by rewriting $ax+b=a\left(x+\frac{b}{a}\right)$.

The dependent variable giving the output of a function; on a graph it is the vertical coordinate of each point.