ALGRZ.MATH.6.A

Estimate a reasonable input value that results in a given output value for a given function, including quadratic, rational, and exponential functions.

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

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Vocabulary
input valueoutput valuefunctionquadratic functionsrational functionsexponential functions
Skills
  • estimate (reasonable input given output and a function) #dok2
  • identify (appropriate input values for given output values) #dok2
  • apply (estimation strategies with quadratic, rational, and exponential functions) #dok2
  • analyze (relationships between inputs and outputs in functions) #dok2
  • relate (real-world contexts to functional relationships) #dok2
Learning Targets
  • I can define the terms input value and output value as they relate to a function. #dok1
  • I can describe the difference between quadratic, rational, and exponential functions. #dok1
  • I can identify a given input or output value from a function table or graph. #dok1
  • I can estimate a reasonable input value that produces a specified output in a quadratic function. #dok2
  • I can estimate a reasonable input value that produces a specified output in a rational function. #dok2
  • I can estimate a reasonable input value that produces a specified output in an exponential function. #dok2
  • I can apply estimation to solve real-world problems involving input and output values of functions. #dok2
  • I can justify my reasoning for selecting a particular input value for a given output value. #dok3
  • I can explain my estimation methods and evaluate their accuracy in context. #dok3
Big Ideas
  • A function connects input values to output values according to specific mathematical rules.
  • Understanding how to estimate input values for given outputs in various function types helps model and solve real-world problems.
Essential Questions
  • How can you determine what input will produce a certain output in a quadratic, rational, or exponential function?
  • What strategies can be used to estimate input values when an exact answer is not easily found?
  • Why is it important to estimate reasonable input values in real-world situations?
  • How do the characteristics of different types of functions (quadratic, rational, exponential) affect your estimation process?
  • In what situations would knowing how to estimate input values for functions be particularly useful?