ALG2.MATH.6.K

Determine the asymptotic restrictions on the domain of a rational function and represent domain and range using interval notation, inequalities, and set notation.

Algebra II · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

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Vocabulary
asymptotic restrictionsdomainrational functioninterval notationinequalitiesset notationrange
Skills
  • determine (asymptotic restrictions on the domain of a rational function) #dok2
  • represent (domain of a rational function using interval notation, inequalities, and set notation) #dok2
  • represent (range of a rational function using interval notation, inequalities, and set notation) #dok2
  • identify (vertical asymptotes and values excluded from domain) #dok1
  • analyze (the relationship between asymptotes and domain/range) #dok3
Learning Targets
  • I can identify vertical asymptotes and values excluded from the domain of a rational function. #dok1
  • I can determine the asymptotic restrictions on the domain of a rational function. #dok2
  • I can represent the domain of a rational function using interval notation, inequalities, and set notation. #dok2
  • I can represent the range of a rational function using interval notation, inequalities, and set notation. #dok2
  • I can analyze how the asymptotes of a rational function affect its domain and range. #dok3
Big Ideas
  • The domain of a rational function is determined by the values that make the denominator nonzero, often resulting in asymptotes.
  • Interval notation, inequalities, and set notation provide multiple ways to describe the domain and range of rational functions, highlighting mathematical precision and reasoning.
Essential Questions
  • How do asymptotes impact the domain and range of a rational function?
  • What are the different ways to represent the domain and range of a rational function?
  • Why are some values excluded from the domain of a rational function?
  • How can you determine the asymptotic restrictions for a given rational function?
  • What is the relationship between a rational function’s algebraic expression and its graph’s asymptotic behavior?