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vertical asymptote

comes from a factor in the denominator that doesnt cancel out

hole in graph

comes from factor in the denominator that cancels with the same factor in the numerator

horizontal asymptote

a line that the curve approaches as x goes to infinity but never reaches

least common multiple

The smallest multiple (other than zero) that two or more numbers have in common.

Complex Fraction

A fraction that contains one or more fractions in its numerator or denominator.

restricted value

any value that makes the bottom of a rational function equal zero

extraneous root

a solution to a transformed equation that is not a solution of the original equation

rational equation

an equation in one variable containing one or more rational expressions

Rational Expression

an algebraic fraction whose numerator and denominator are polynomials

rational function

a function which is the ratio of 2 polynomials

reciprocal

One of two numbers whose product is 1; it is also called multiplicative inverse.

reduced form

most simpliest form

Domain

The ______________________ is all the possible INPUT, X, values.

Range

The difference between the greatest number and the least number in a set of data.

slant asymptote

occurs when the degree of the top is higher than the degree of the bottom

1.) Add or subtract the numerators

Adding / Subtracting Rational Expressions (With common denominators)

1.) Find the LCD

Adding / Subtracting Rational Expressions (With uncommon denominators)

Complex Rational Expressions

1.) Simplify the numerator and the denominator as if they were separate expression

Solving Rational Equations

-If its a proportion

Rational Expression Word Problem

It takes Steve and Ryan each 2 hours to clean a car. It takes 3 hours for Brad to clean a car. How long will it take for them to clean 7 cars if they work together.

Asymptote

An imaginary line on a graph that acts as a boundary line.

Branch

Each part of the graph of a reciprocal function.

Non-removable Discontinuity

Occurs when factors in the denominator of a rational expression are not cancelled.

Point of Discontinuity

A hole or break in a graph.

continuous graph

A graph with no holes, jumps, or breaks.

Removable discontinuity

Occurs when common factors are cancelled in a rational expression.

Discontinuous Graph

A graph that has holes, jumps, or breaks.

Reciprocal Function

A function in which a variable occurs in the denominator but not in the numerator.