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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.