Today in Pre-Calculus Go over homework Notes: Homework

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Presentation transcript:

Today in Pre-Calculus Go over homework Notes: Homework Graphs of rational functions Homework

Graphs of Rational Functions The line x = a is a vertical asymptote of the graph f(x) if The line y = b is a horizontal asymptote of the graph of f(x) if, vertical asymptote at x = 0 horizontal asymptote at y = 0

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 at If: horizontal asymptote: y=0 horizontal asymptote: y=ratio of leading coefficients no horizontal asymptote

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.

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.

Example 1 List the asymptotes and intercepts for the following graph. Vertical asymptote: none Horizontal asymptote: y=0 Slant asymptote: none x-intercept: none y-intercept: (0,4)

Example 2 List the asymptotes and intercepts for the following graph. Vertical asymptote: x = –1 Horizontal asymptote: none Slant asymptote: y = x – 2 x-intercept: (0,0),(1,0) y-intercept: (0,0)

Example 3 List the asymptotes and intercepts for the following graph. Vertical asymptote: x = –2 , 2 Horizontal asymptote: y=3 Slant asymptote: none x-intercept: (0,0) y-intercept: (0,0)

Homework Pg. 245: 23-30all Chapter 2 test: Tuesday, November 25