12-03: Rational Functions

________ (minus remainder if applicable) is the OA.

Obtained through the division of polynomials Sometimes there’s an x in the numerator

There is always an x in the denominator

No passing through asymptotes, no right angles, no curving back on yourself

Cancelled terms are what create ________.

Obtained through the division of polynomials

to the top of the number means to the left of (think of it as a number line)

no x in numerator, HA y=0)

for the -∞ you put -100 and for ∞ you put 100

fill out the sketch while going through the process of finding all of the highlighted attributes

if there is no x in the numerator, there is no x intercept

sub 0 in for y (f(0)) and solve

Domain ≠ VA, Range ≠ HA

slope analysis is a rate of change

no x in numerator, HA y=0)

for the -∞ you put -100 and for ∞ you put 100

fill out the sketch while going through the process of finding all of the highlighted attributes

if there is no x in the numerator, there is no x intercept

sub 0 in for y (f(0)) and solve

Domain ≠ VA, Range ≠ HA

slope analysis is a rate of change

solve numerator = 0

solve denominator = 0

for the -∞ you put -100 and for ∞ you put 100

y=a/c

fill out the sketch while going through the process of finding all of the highlighted attributes

cannot equal VA, skip over asymptote

cannot equal HA, skip over asymptote

slope analysis is a rate of change

multiply, expand, solve

factor, common denominator

then use the interval table to determine what is appropriate for the question

this is the x value of your holes coordinate → to find the y value of your hole, plug x into f(x) and solve

see that nothing cancels and you dont have a hole

Set denominator to 0

make holes