MYP Extended Mathematics Sequences, Rational Expressions and Equations Key Definitions

A sequence in which the difference between consecutive terms is constant.

The constant value $d$ such that $u_{n+1}-u_n=d$ for every term in an arithmetic sequence.

The constant multiplier $r$ in a geometric sequence, found by dividing a term by the previous term: $r=\frac{u_{n+1}}{u_n}$.

A value found while solving an equation algebraically that does not satisfy the original equation (often because it makes a denominator zero).

A sequence in which the ratio between consecutive terms is constant (each term is found by multiplying the previous term by the same number).

A horizontal line $y=c$ that a graph approaches as $x\to +\infty$ and/or $x\to -\infty$.

An expression of the form $\frac{P(x)}{Q(x)}$, where $P(x)$ and $Q(x)$ are polynomials and $Q(x)\neq 0$.

An equation that includes one or more rational algebraic expressions.

A restriction is any value of the variable that is not allowed because it makes the denominator zero.

A vertical line $x=c$ that a graph approaches as the input approaches $c$. For rational functions, it often occurs where the denominator approaches 0.