1. Warm Up - Factor the following completely : 1. 3x 2 -8x+4 2. 11x 2 -99 3. 16x 3 +128 4. x 3 +2x 2 -4x-8 5. 2x 2 -x-15 6. 10x 3 -80 (3x-2)(x-2) 11(x+3)(x-3) 16(x+2)(x 2 -2x+4) (x-2)(x+2) 2 (2x+5)(x-3) 10(x-2)(x 2 +2x+4)

2. Graphing General Rational Functions Goal: Graph general rational functions. Goal: Use the graph of a rational function to solve real-life problems.

3. Yesterday, we graphed rational functions where x was to the first power only. What if x is not to the first power? Such as:

4. Steps to graph when x is not to the first power 1. Find the x-intercepts. (Set numerator =0 and solve) 2. Find vertical asymptote(s). (set denominator =0 and solve) 3. Find horizontal asymptote. 3 cases: a. If degree of top < degree of bottom, y=0 b. If degrees are =, c. If degree of top > degree of bottom, no horizontal asymptote, but there will be a slant asymptote. 4. Graph asymptotes, intercepts, and connect with curves. 5.Check solutions on calculator.

5. Determine the key features and then draw the graph. x-intercepts _____________ vertical asymptote: _______ Domain:_______ horizontal asymptote: ______ Range: _______

6. Determine the key features and then draw the graph. x-intercepts _____________ vertical asymptote: _______ Domain:_______ horizontal asymptote: ______ Range: _______

7. Determine the key features and then draw the graph. x-intercepts _____________ vertical asymptote: _______ Domain:_______ horizontal asymptote: ______ Range: _______

8. Determine the key features and then draw the graph. x-intercepts _____________ vertical asymptote: _______ Domain:_______ horizontal asymptote: ______ Range: _______

9. Assignment Rational Functions Worksheet 2