Unit 1 B Flashcards
what is a rational function?
a ratio of polynomials that could have horizontal vertical, or slant asymptotes
end behavior for a rational function always refers to…
horizontal asymptotes
if numerator’s degree is less than denominator’s degree
the HA is at y=0
as x > +/- inf f(x)=0
if numerator’s degree is equal to denominator’s degree
the HA is at leading co of num/leading co of de
as x > +/- inf f(x)=a/b
if numerator’s degree is more than denominator’s degree
no HA
as x > +/- inf f(x)=+/- inf
if the degree of the numerator is exactly one more than the degree of the denominator…
f(x) has a slant (oblique) asymptote
slant asymptotes…
are parallel to y=a/bx (same slope)
a rational function will have zeros where…
the numerator is zero
a rational function will have vertical asymptotes where…
the denominator is zero
the f(x) and g(x) share a factor that will be…
a whole in the graph
to solve rational inequalities…
find zeros and VAs, use sign chart, test points
to subtract fractions you must…
first find a LCD
vertical asymptotes are…
factors in the denominator that don’t cancel
limits when there is a whole
equal hole
limits with VA
+/- inf
when writing an equation…
find holes and vas, make sure wholes add up, make sure multiplicity is correct for VAs (if same sign for limits should be even)
when squaring an exponent
square the coefficient too
when making sign charts always include
holes
binomial theorem
(a+b)^n= (n choose zero up to n choose n) (a to the n to a to the zero) (b to the zero to b to the n)
paschal’s triangle
row one is for zero, start with one and add down
domain of a rational function
everything except holes and VAs
to find a slant asymptote..
perform division (can disregard remainder)
vertical shift
f(x)+k
horizontal shift
f(x+k)
horizontal transformations act…
opposite to how you would think they would
vertical dilation
a*f(x) (take abs. value of a)
if a is negative will be a reflection over the x axis
horizontal dilation
f(ax) (by a factor of 1/b)
if b is negative it will be a reflection over the y axis
linear
constat roc
quadratic
2nd diff constant
inverse variation
y=k/x
k is a constant of proportionality
