Sketch the graph of $y = \frac { 1 } { x }$. .

1. Why does this graph have a vertical asymptote? What is the equation of that asymptote?

   Hint (a):

   Consider your answer to 1-26(d).

   More Help (a):

   Vertical asymptotes are lines with undefined slopes. Their equations are of the form: $x = k$ where $k$ is a constant.

2. State the equation of the horizontal asymptote.

   Hint (b):

   Consider the horizontal lines that you found in problem 1-22(b).

   More Help (b):

   Horizontal asymptotes are lines with $0$ slope. Their equations are of the form: $y = 0x+b$ or $y = k$, where $k$ is some constant.

3. Alter$y = \frac { 1 } { x }$ so that the vertical asymptote is $x = 1$ and the horizontal asymptote is $y = 3$.

   Hint (c):

   $y=\frac{1}{x-h}+k$