1. Lesson 2.6 Rational Functions and Asymptotes

2. Graph the function: Domain: Range: Increasing/Decreasing: Line that creates a split in the graph:

3. Rational Functions Where N(x) and D(x) are polynomials Discontinuities: places where the graph “skips” or “jumps” Graph and look for discontinuities:

4. Discontinuities Hole: can be factored out Jumps: cannot be factored out Asymptotes (jumps) A horizontal or vertical line through which a graph is undefined Cannot be factored out

5. Finding location of asymptotes: Given ; n = degree of N(x), d = degree of D(x) Vertical asymptote(s): At zeros of D(x); Write “x = #” Horizontal asymptote(s): If n < d → → y = 0 If n = d →→ If n > d →→ no horizontal asymptote

6. Example Find all discontinuities of Problem Set 2.6