Rational Functions

  1. \rhd  Graphing rational functions according to asymptotes (11:21)  Finding the horizontal and vertical asymptotes of \dfrac{3x^2-18x-81}{6x^2-54}.
  2. \rhd Graphs of rational functions: y-intercept (3:07) Given four graphs, identify the graph of the function f(x)=\dfrac{ax^n+bx+12}{cx^m+dx+12} by finding its y-intercept.
  3. \rhd Graphs of rational functions: horizontal asymptote (3:15) Given four graphs, identify the graph of the function f(x)=\dfrac{-x^2+ax+b}{x^2+cx+d} by finding its horizontal asymptote.
  4. \rhd Graphs of rational functions: vertical asymptote (5:33) Given four graphs, identify the graph of the function f(x)=\dfrac{g(x)}{x^2-x-6} where g(x) is a polynomial by finding its vertical asymptote.
  5. \rhd Graphs of rational functions: zeros (7:46) Given four graphs, identify the graph of the function f(x)=\dfrac{3x^2-18}{g(x)} where g(x) is a polynomial by finding its zeros.
  6. * Practice problem: Type of problem: Identify the graph of \dfrac{15x^3+b}{3x^3+cx+d} where b, c and d are unknown constants.