Unit 2: Polynomial and Rational Functions Flashcards
n is the (blank) of the polynomial
degree
leading coefficient
Relative maximum is when…
a function changes from increasing to decreasing
Relative minimum is when…
a function changes from decreasing to increasing
Absolute maximum is…
the highest y-value of the function at some x
Absolute minimum is…
the lowest y-value of the function at some x
The degree of the polynomial is equal to…
the constant nth difference
relative extrema are also called…
local extrema
absolute extrema are also called…
global extrema
Inflection point
where function changes concavity
multiplicity is…
the number of times a factor occurs
If multiplicity is one…
If multiplicity is three…
If multiplicity is even…
How many zeros can a polynomial have?
The same as the degree including multiplicity
quadratic formula
complex zeros come in…
conjugate pairs
Even function is symmetric…
over the y-axis
Odd function is symmetric…
about the origin
For an even function plugging in opposite x-values will give you…
same y-values
For an odd function plugging in opposite x-values will give you…
opposite y-values
What type of end behavior is this?
Left end behavior
What type of end behavior is this?
Right end behavior
Describe left end behavior verbally
“As the x values decrease without bound, the y values of f(x)…”
Describe right end behavior verbally
“As the x values increase without bound, the y values of f(x)…”
If function has a positive leading coefficient then…
the right end goes to infinity
If function has a negative leading coefficient then…
the right end goes to negative infinity
If the degree of the polynomial is even then…
the left end goes in the same direction as the right end
If the degree of the polynomial is odd then…
the left end goes in the opposite direction as the right end
(x , y) -> ( -x , y ) is what type of function?
even because opposite x values give same y values
(x , y) -> (-x , -y) is what type of function?
opposite because opposite x values give opposite y values
Rational functions are…
a ratio of two polynomials
When does a rational function have a horizontal asymptote at y=a/b?
When the leading terms in the numerator and denominator have the same degree
n=d
When does a rational function have a horizontal asymptote at y=0?
When the degree of the numerator is less than the degree of the denominator
n<d
When does a rational function have a slant asymptote?
When degree of the numerator is exactly 1 more than the degree of the denomiator
n=d+1
When does a rational function have no horizontal asymptote?
When the degree in the numerator is greater than the degree in the denominator
n>d
graphs of rational functions can never cross…
vertical asymptotes
A rational function has an x-intercept when…
the number where ONLY the factor in the numerator is zero
a rational function has a hole when…
same factor is in numerator and denominator
a rational function has a vertical asymptote when…
the number where ONLY the factor in the denominator is zero
rational functions can represent…
division problems
Here shows the division of a rational function. Name each part of the division.
How do you know if a rational function has a slant asymptote?
A slant asymptote occurs if the quotient function is a linear function.
Build Pascal’s Triangle for a binomial expansion to the 7th power.
