1. 2.5 RATIONAL FUNCTIONS DAY 2 Learning Goals – Graphing a rational function with common factors.

2. Warm-up Given the Rational Function, Find the domain Find the vertical asymptote(s) Find the horizontal asymptotes Find the y-intercept Find the x-intercept(s) Sketch the graph

3. Warm-up Given the Rational Function, Find the domain Find the vertical asymptote(s), x = 0, x = 5, x = -2 Find the horizontal asymptotes y = 0 Find the y-intercept None Find the x-intercept(s) x = -6, x = -4 Sketch the graph Test Point (-5, 1/150) -6 -4 -2 0 5 - + - + - +

4. Graphing Rational Functions with Common Factors Similar to 2.5 Day 1. **New** Factor the Numerator and Denominator completely. **New** Check for Common Factors and Simplify THIS FACTOR WILL LEAVE A REMOVABLE DISCONTINUITY, OR HOLE AT X=C!!! Continue as before – Vert. and Horz. Asymptotes, Zeros, Test Intervals, Find Critical Points, if needed. Mark the hole. Homework – 138: 7, 8, 22, 26, 28