For each part below, give an example of a function with specified attributes. Provide a sketch of each function.

1. A function with a hole at $x = 3$ and an asymptote at $x = -1$.

   Hint (a):

   Write a rational function with ($x - 3$) in both the numerator and the denominator to make a hole at $x = 3$.

   More Help (a):

   Remember that vertical asymptotes are formed by zeros in the denominator.

2. A function with asymptotes at the $y$-axis and $x = 5$ and a hole at $x = -4$.

   Hint (b):

   An asymptote at the $x$ axis is the same as having a vertical asymptote of $x = 0$.

3. A function with an end behavior function $g(x) = 3x - 1$.

   Hint (c):

   Holes and vertical asymptotes do not affect end behavior. How can $y = 3x -1$ be altered so that it has a hole or vertical asymptote?

   Answer (c):

   Possible answer: $y = 3x - 1 +$ [answer to part (a)]