PRECAL.MATH.2.J

Analyze and describe end behavior of functions, including exponential, logarithmic, rational, polynomial, and power functions, using infinity notation to communicate this characteristic in mathematical and real-world problems; Page 14 October 2015 Update.

Precalculus · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
end behaviorfunctionsexponential functionslogarithmic functionsrational functionspolynomial functionspower functionsinfinity notationmathematical problemsreal-world problems
Skills
  • analyze (end behavior of exponential, logarithmic, rational, polynomial, and power functions) #dok2
  • describe (end behavior of functions using infinity notation) #dok2
  • apply (analysis of end behavior to mathematical and real-world problem scenarios) #dok3
  • communicate (end behavior using proper mathematical language and notation) #dok1
Learning Targets
  • I can identify the end behavior of exponential, logarithmic, rational, polynomial, and power functions. #dok1
  • I can recognize infinity notation and its meaning when describing end behavior. #dok1
  • I can describe the end behavior of given functions using infinity notation. #dok2
  • I can analyze the equations or graphs of functions to determine their end behavior. #dok2
  • I can apply my understanding of end behavior to solve mathematical and real-world problems. #dok3
  • I can justify my interpretation of a function’s end behavior using mathematical evidence. #dok3
Big Ideas
  • End behavior reveals how functions behave as the input becomes extremely large or small, which is crucial for understanding their long-term trends.
  • Infinity notation provides a precise way to communicate the end behavior of functions in both mathematical analyses and real-world modeling.
Essential Questions
  • What does end behavior of a function tell us about the function's graph as x approaches positive or negative infinity?
  • How can infinity notation be used to describe and communicate the end behavior of different types of functions?
  • How does understanding end behavior help in predicting real-world phenomena modeled by functions?
  • How do different families of functions (exponential, logarithmic, rational, polynomial, power) compare in their end behaviors?
  • In what situations is it important to analyze or communicate the end behavior of functions using precise mathematical language?