12-03: Rational Functions

Quotient

________ (minus remainder if applicable) is the OA.

Rational function

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

holes

Cancelled terms are what create ________.

Rational function

Obtained through the division of polynomials

a little + at the top of the number means to the right of, a little

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

Find HA, with reciprocals of linear functions, your HA will be y=0 (rule

no x in numerator, HA y=0)

The test values you will use for the VA will be one decimal to the left (for VA⁻⁻) and one decimal to the right (for VA⁺); the test values you use for HA

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

Sketch

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

Find x intercept

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

Find y intercept

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

Domain and range

Domain ≠ VA, Range ≠ HA

Analyze slopes

slope analysis is a rate of change

Find HA, with reciprocals of linear functions, your HA will be y=0 (rule

no x in numerator, HA y=0)

The test values you will use for the VA will be one decimal to the left (for VA⁻⁻) and one decimal to the right (for VA⁺); the test values you use for HA

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

Sketch

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

Find x intercept

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

Find y intercept

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

Domain and range

Domain ≠ VA, Range ≠ HA

Analyze slopes

slope analysis is a rate of change

Find x intercept

solve numerator = 0

Find VA

solve denominator = 0

The test values you will use for the VA will be one decimal to the left (for VA⁻⁻) and one decimal to the right (for VA⁺); the test values you use for HA

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

Find HA

y=a/c

Sketch

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

Domain

cannot equal VA, skip over asymptote

Range

cannot equal HA, skip over asymptote

Analyze slopes

slope analysis is a rate of change

Clear your fractions

multiply, expand, solve

Simplify to a single fraction

factor, common denominator

Look back to the original question and see what it is asking

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

Restrict (make = to 0) the term that youre cancelling

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

Factor

see that nothing cancels and you dont have a hole

VA

Set denominator to 0

Cancelled terms

make holes