Unit 2 Continued Flashcards
Linear Factors are in the form…
(x + a) or (x-a)
they indicate a root
Another name for a removable discontinuity
A hole in the graph
ordered pair?
A coordinate. ie: (x,y)
How do you find a removable discontinuity in a Rational Function
when you can cancel out a factor in the numerator and denominator, a hole exists at whatever x value makes this factor a zero.
How do you determine the roots for a Rational Function ?
you set the numerator equal to zero (sometimes factor) and solve for x.
How do you determine vertical asymptotes in a Rational Function
Vertical you find the factors in the denominator that don’t cancel out, set them equal to zero, and solve for x.
What is another name for a root?
A zero (because y = 0 at a root)
How do you find the degree of a polynimial ?
you look at the largest exponent in the function. example: second degree polynomial
There is a horizontal asymptote at y=0 if…
the degree of the numerator is less than the degree of the denominator.
example:
Irreducible quadratic factor
a quadratic that cannot be broken down into linear factors
ex:
How do we find the multiplicity of a zero in a factored function
you find the linear factor that is associated with the zero and look at the exponent on that factor.
example: if f(x) has a root at (-A,0)
then (x+A) is a factor of f(x).
and if f(x) = (x+A)3 + (x-B)2
then the multiplicity of the root (-A,0) is 3.
if the degree of the numerator is equal to the degree of the denominator….
there will be a horizontal asymptote at y = ratio of leading coefficients.
example: there is a horizontal asymptote at y = 4/3 for the following rational function:
if the degree of the numerator is one more than the degree of the denominator….
there is no horizontal asymptote, instead there is an oblique (slant) asymptote
You can find the slant asymptote using long division of the numerator divided by the denominator.
