We can use arrow notation to describe local behavior and end behavior of the toolkit functions
and
See
[link] .
A function that levels off at a horizontal value has a horizontal asymptote. A function can have more than one vertical asymptote. See
[link] .
Application problems involving rates and concentrations often involve rational functions. See
[link] .
The domain of a rational function includes all real numbers except those that cause the denominator to equal zero. See
[link] .
The vertical asymptotes of a rational function will occur where the denominator of the function is equal to zero and the numerator is not zero. See
[link] .
A removable discontinuity might occur in the graph of a rational function if an input causes both numerator and denominator to be zero. See
[link] .
A rational function’s end behavior will mirror that of the ratio of the leading terms of the numerator and denominator functions. See
[link] ,
[link] ,
[link] , and
[link] .
Graph rational functions by finding the intercepts, behavior at the intercepts and asymptotes, and end behavior. See
[link] .
If a rational function has
x -intercepts at
vertical asymptotes at
and no
then the function can be written in the form
t he silly nut company makes two mixtures of nuts: mixture a and mixture b. a pound of mixture a contains 12 oz of peanuts, 3 oz of almonds and 1 oz of cashews and sells for $4. a pound of mixture b contains 12 oz of peanuts, 2 oz of almonds and 2 oz of cashews and sells for $5. the company has 1080
Lairene and Mae are joking that their combined ages equal Sam’s age. If Lairene is twice Mae’s age and Sam is 69 yrs old, what are Lairene’s and Mae’s ages?