Chapter 8 - Rational Expressions and Equations

Graph Rational Functions

If a number is both a zero of the numerator and denominator, it is a point of discontinuity To ________: 1.

Inverse variation

________- expressed as 𝑦= 𝑘/𝑥; as one quantity increases, the other quantity decreases.

Rational functions

________ may have breaks in continuity; they can not be traced with a pencil never leaving the paper- Breaks occur at values that are excluded from the domain- Breaks can appear as point discontinuity or asymptotes An asymptote- a line that the graph of a function approaches, but never touches.

Rational expression

a ratio of two polynomial expressions

Complex fraction

a rational expression whose numerator and/or denominator contains a rational expression

asymptote

a line that the graph of a function approaches, but never touches

Point discontinuity

a hole in a graph

Direct variation

expressed as 𝑦 = 𝑘𝑥; intercepts the y-axis at 0

Joint variation

expressed as 𝑦 = 𝑘𝑥𝑧; occurs when one quantity varies directly as the productof two or more other quantities

Rational equation

any equation that contains one or more rational expressions

Rational inequalities

inequalities that contain one or more rational expressions