Equivalent Algebraic Expressions Flashcards
Natural numbers
Counting numbers
While numbers
Counting numbers plus zero
Integers
I or Z
Positive and negative whole numbers plus zero
Rational numbers
Q
Numbers inform a/b a and b are integers and b cannot be zero
Irrational numbers
Any numbers that cannot be expressed by a/b
Real numbers
All rational and irrational numbers
E rulers number
Complex numbers
Square roots of negatives
Whole numbers also included
Polynomial
Where a are coefficients that are real numbers and the exponents are whole numbers
Factoring
Process of expressing and expression into a series of factors
A factored state will be one in which there are factors multiplying each other without plus or minus
Rational expressions
An expression in which a polynomial is divided by another polynomial
Point/ removable discontinuity
Occurs when a factor in the numerator has a matching factor in the denominator
The restriction is he home
Rational functions
As x moves to infinity f(x) moves to ward zero
And as x moves to negative infinity f(x) moves to zero
Verticals asymptote
Occurs when restriction causes denominator to be 0 while numerator is not
There is no pair in the numerator
The asymptote occurs at restriction x=5/2
Degree of the denominator is larger than numerator
Horizontal asymptote at y=o
Bottom is growing larger than top
F(x) cannot be zero
Degree of denominator = degreee of numerator
Horizontal asymptote at coefficients of the highest degrees a/b
As x approaches positive and negative infinity, y approaches a/b
