Further rational functions

Factor numerator and denominator first, retaining every original exclusion. A remaining denominator zero usually produces a vertical asymptote; a cancelled factor can produce a hole. **Example** | **Asymptotes and intercepts** x+1x2-4 | x=+-2, y=0; (-1,0), (0,- 14) x2+1x-1=x+1+ 2x-1 | x=1, y=x+1; (0,-1), no real zero Compare degrees for horizontal asymptotes; divide a quadratic numerator by a linear denominator for an oblique asymptote. Sketch each branch separately and check its approach on both sides of every vertical asymptote.