ALGRZ.MATH.7.B

Compare and contrast between the mathematical and reasonable domain and range of functions modeling real-world situations, including linear, quadratic, exponential, and rational functions.

Algebraic Reasoning · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
mathematical domainmathematical rangereasonable domainreasonable rangefunctionsreal-world situationslinear functionsquadratic functionsexponential functionsrational functions
Skills
  • compare (mathematical and reasonable domains and ranges of functions) #dok2
  • contrast (mathematical and reasonable domains and ranges of functions) #dok2
  • identify (mathematical domain and range of linear, quadratic, exponential, and rational functions) #dok1
  • identify (reasonable domain and range based on real-world context) #dok2
  • justify (selection of mathematical or reasonable domain/range in context) #dok3
Learning Targets
  • I can identify the mathematical domain and range of linear, quadratic, exponential, and rational functions. #dok1
  • I can identify the reasonable domain and range of a function based on its real-world context. #dok2
  • I can compare and contrast the mathematical and reasonable domains and ranges of functions modeling real-world situations. #dok2
  • I can justify the choice of a reasonable domain and range for a given real-world application. #dok3
Big Ideas
  • The domain and range of a function can differ depending on whether considered mathematically (all possible inputs/outputs) or within a real-world context (what actually makes sense in the situation).
  • Comparing mathematical and reasonable domains/ranges deepens understanding of how functions model real phenomena and builds the ability to apply math to real-life situations.
Essential Questions
  • How do you determine the mathematical domain and range for a function?
  • In what ways might the reasonable domain and range for a real-world scenario differ from the mathematical domain and range?
  • Why is it important to distinguish between the mathematical and reasonable domain and range when modeling real-world situations?
  • How can you justify your choice of a reasonable domain and range in a real-world application?
  • What strategies can you use to identify unreasonable domains or ranges for real-world contexts?