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
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