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Grade 11 Math Lab: Transcendence & Limits FREE

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Rational Functions

65 min Grade 11 Math Lab: Transcendence & Limits

Learning Objectives

  • Find asymptotes
  • Analyze discontinuities
  • Graph rational functions

Key Concepts

Vertical Asymptote

Where denominator = 0

Horizontal Asymptote

End behavior as x → ±∞

Theory

For f(x) = p(x)/q(x): **Vertical Asymptotes:** Set q(x) = 0 **Horizontal Asymptotes:** - Degree p < Degree q: y = 0 - Degree p = Degree q: y = (leading coefficients) - Degree p > Degree q: No HA (oblique asymptote)

Examples

Find asymptotes of f(x) = (2x)/(x-3)

Solution: VA: x = 3, HA: y = 2