Presentation on theme: "Today in Pre-Calculus Go over homework Notes: Homework"— Presentation transcript:
1 Today in Pre-Calculus Go over homework Notes: Homework Graphs of rational functionsHomework
2 Graphs of Rational Functions The line x = a is a vertical asymptote of the graph f(x) ifThe line y = b is a horizontal asymptote of the graph of f(x) if,vertical asymptote at x = 0horizontal asymptote at y = 0
3 Graphical Features of Rational Functions Vertical Asymptotes: occur at the zeros of the denominator provided they are not also zeros of the numerator of equal or greater multiplicity.Horizontal Asymptotes: look atIf:horizontal asymptote: y=0horizontal asymptote: y=ratio of leading coefficientsno horizontal asymptote
4 Graphical Features of Rational Functions Slant (or Oblique) Asymptotes: occur if the degree of numerator is exactly one more than the degree of denominator. Use polynomial long division, the quotient is the equation for the slant asymptote.Note: Graphs NEVER intersect their vertical asymptotes but they can intersect slant and horizontal asymptotes.
5 Graphical Features of Rational Functions X-intercepts: Occur when f(x) equals 0 (basically when the numerator equals 0, provided this is not also a zero of the denominator).Y-intercepts: Occur at f(0), if defined.
6 Example 1 List the asymptotes and intercepts for the following graph. Vertical asymptote: noneHorizontal asymptote: y=0Slant asymptote: nonex-intercept: noney-intercept: (0,4)
7 Example 2 List the asymptotes and intercepts for the following graph. Vertical asymptote: x = –1Horizontal asymptote: noneSlant asymptote: y = x – 2x-intercept: (0,0),(1,0)y-intercept: (0,0)
8 Example 3 List the asymptotes and intercepts for the following graph. Vertical asymptote: x = –2 , 2Horizontal asymptote: y=3Slant asymptote: nonex-intercept: (0,0)y-intercept: (0,0)
9 HomeworkPg. 245: 23-30allChapter 2 test: Tuesday, November 25