PRECAL.MATH.2.I

Determine and analyze the key features of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions, including step functions such as domain, range, symmetry, relative maximum, relative minimum, zeros, asymptotes, and intervals over which the function is increasing or decreasing.

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

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Vocabulary
key featuresexponential functionslogarithmic functionsrational functionspolynomial functionspower functionstrigonometric functionsinverse trigonometric functionspiecewise defined functionsstep functionsdomainrangesymmetryrelative maximumrelative minimumzerosasymptotesintervalsfunctionincreasingdecreasing
Skills
  • determine (key features of various functions) #dok2
  • analyze (key features for multiple types of functions) #dok3
  • describe (domain, range, symmetry, extrema, zeros, asymptotes, intervals of change) #dok2
  • compare (behavior among different families of functions) #dok3
  • interpret (the significance of key features in real-world and mathematical contexts) #dok3
Learning Targets
  • I can identify domains and ranges of exponential, logarithmic, rational, polynomial, power, trigonometric, inverse trigonometric, and piecewise defined functions. #dok1
  • I can list zeros, asymptotes, and intervals of increase or decrease from a function's graph or equation. #dok1
  • I can describe the symmetry, maximums, minimums, and other key features of given functions. #dok2
  • I can determine and justify the intervals over which a function is increasing or decreasing. #dok2
  • I can analyze and explain how key features such as zeros, asymptotes, and extrema affect the behavior of a function. #dok3
  • I can interpret how the key features of a function relate to real-world contexts or mathematical problems. #dok3
Big Ideas
  • Key features of functions, such as domain, range, zeros, extrema, asymptotes, and intervals of change, are essential for understanding and comparing different families of functions.
  • Analyzing the graphical and algebraic representations of functions enables deeper insight into their behaviors and applications to real-world scenarios.
Essential Questions
  • What key features can we use to describe and compare the behaviors of different types of functions?
  • How do the features such as zeros, asymptotes, and extrema inform us about a function's graph and real-world meaning?
  • Why is it important to determine where a function is increasing or decreasing?
  • How does understanding domain and range help us analyze or solve real-world problems involving functions?
  • In what ways do symmetry and other properties of a function's graph enhance our understanding of mathematical relationships?