1. Graphing Rational Functions

2. Investigation
Graph the following: 1. y = 3/x 2. y = 6/x 3. y = -8/x 4. y = -4/x What do you notice?!?!?

3. Rational Functions
Rational functions in the form y = k/x are split into two parts. Each part is called a BRANCH. If k is POSITIVE the branches are in Quadrants I and III If k is NEGATIVE the branches are in Quadrant II and IV

4. Asymptotes
An asymptote is a line that the graph approaches but NEVER touches!

5. Find the asymptotes!

6. Simple Rational Functions
the vertical asymptote is x = b
the horizontal asymptote is y = c

7. Identify the asymptotes from the following functions:

8. Translating Rational Functions
Translate
Up 3 units and left 2 units
2. Down 5 units and right 1 unit
3. Right 4 units
4. Such that it has a vertical asymptote of x=3 and a horizontal asymptote of y= -2