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Level 393

Rational Expressions & Functions


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rational function
a function which is the ratio of 2 polynomials
Asymptote
An imaginary line on a graph that acts as a boundary line.
vertical asymptote
comes from a factor in the denominator that doesnt cancel out
horizontal asymptote
a line that the curve approaches as x goes to infinity but never reaches
Linear Function
y = mx + b
Quadratic Function
a function that can be written in the form f(x)=ax^2+bx+c, where a, b & c are real numbers and a is not equal to zero
Absolute Value Function
any f(x) = | x |
Exponential Function
y = ab^x
square root function
a function that contains the independent variable in the radicand
Rational Expression
an algebraic fraction whose numerator and denominator are polynomials
multiplying rational expressions
P/Q x R/S = PR/QS ; 1. factor 2. multiply 3. and simplify
dividing rational expressions
P/Q / R/S = P/Q x S/R = PS/QR ; 1. factor 2. opposite reciprocal 3. multiply 4. and simplify
divide a polynomial by a monomial
use distributive property to divide each term of the polynomial by the monomial
divide a polynomial by a binomial
use long division and align terms by their degrees; for each missing power, add a term into dividend with 0 as its coefficient
hole in graph
comes from factor in the denominator that cancels with the same factor in the numerator
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
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