ALGRZ.MATH.3.C

Verify that two functions are inverses of each other tabularly and graphically such as situations involving compound interest and interest rate, velocity and braking distance, and Fahrenheit-Celsius conversions.

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

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Vocabulary
functionsinversestablegraphcompound interestinterest ratevelocitybraking distanceFahrenheit-Celsius conversions
Skills
  • verify (two functions are inverses of each other tabularly and graphically) #dok2
  • interpret (real-world contexts where inverse functions apply) #dok2
  • analyze (tables and graphs to determine function-inverse relationships) #dok2
  • explain (the relationship between a function and its inverse in applied contexts) #dok3
Learning Targets
  • I can identify whether two functions are inverses using a table of values. #dok2
  • I can identify whether two functions are inverses using their graphs. #dok2
  • I can interpret real-world situations where inverse functions are used, such as compound interest or Fahrenheit-Celsius conversions. #dok2
  • I can justify how two functions are inverses based on their outputs and inputs in specific examples. #dok3
  • I can explain how applying a function and its inverse returns to the original value in a real-world scenario. #dok3
Big Ideas
  • Inverse functions reverse the effect of the original function and can be verified using tables and graphs.
  • Real-world applications, such as converting temperatures or analyzing financial calculations, often rely on understanding and using inverse functions.
Essential Questions
  • How can you determine if two functions are inverses of each other using a table or a graph?
  • In what real-world contexts might you use inverse functions and why are they important?
  • What does it mean for two functions to 'undo' each other in terms of their outputs and inputs?
  • How can you visually demonstrate that two functions are inverses using graphs?
  • Why must we verify inverses in multiple representations (tabularly and graphically)?