For each part below, give an example of a function with specified attributes. Provide a sketch of each function.
A function with a hole at
and an asymptote at .
Write a rational function with
in both the numerator and the denominator to make a hole at .
Remember that vertical asymptotes are formed by zeros in the denominator.
A function with asymptotes at the
-axis and and a hole at .
An asymptote at the
-axis is the same as having a vertical asymptote of .
A function with an end-behavior function
Holes and vertical asymptotes do not affect end behavior. How can
be altered so that it has a hole or vertical asymptote?