Today in Pre-Calculus

1
Today in Pre-Calculus

• Go over homework
• Notes (NO calculators)
• Graphs of rational functions (no handout)
• Homework

2
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
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 at
• If
• horizontal asymptote y0
• horizontal asymptote yratio of leading
  coefficients
• no 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.

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Example 1

• List the asymptotes and intercepts for the
  following graph.
• Vertical asymptote none
• Horizontal asymptote y0
• Slant asymptote none
• x-intercept none
• y-intercept (0,4)

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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)

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Example 3

• List the asymptotes and intercepts for the
  following graph.
• Vertical asymptote x 2 , 2
• Horizontal asymptote y3
• Slant asymptote none
• x-intercept (0,0)
• y-intercept (0,0)

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Homework

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