ALGRZ.MATH.3.F

Compare and contrast a function and possible functions that can be used to build it tabularly, graphically, and symbolically such as a quadratic function that results from multiplying two linear functions.

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

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Vocabulary
functionpossible functionsquadratic functionlinear functionstabular representationgraphical representationsymbolic representation
Skills
  • compare (a function and possible functions that can be used to build it, using tables, graphs, and symbols) #dok2
  • contrast (a function and possible functions that can be used to build it, using tables, graphs, and symbols) #dok2
  • analyze (compositions of functions, e.g., how linear functions can be combined to form a quadratic function) #dok3
  • represent (functions and their compositions across tables, graphs, and equations) #dok1
Learning Targets
  • I can identify a function and possible functions that can be used to construct it using tables, graphs, or equations. #dok1
  • I can represent a quadratic function as the product of two linear functions symbolically, tabularly, and graphically. #dok1
  • I can compare a function and possible functions that can build it by examining their representations. #dok2
  • I can contrast different ways functions can be built from simpler functions using various representations. #dok2
  • I can analyze the process of constructing a complex function from simpler functions by describing their relationships in multiple representations. #dok3
Big Ideas
  • Complex functions can be built by combining simpler functions, and these relationships can be identified and analyzed through various representations.
  • Comparing and contrasting functions with their component functions allows for deeper understanding of mathematical structures and how representations translate between visual, numerical, and symbolic forms.
Essential Questions
  • How can a complex function be built from simpler functions?
  • In what ways do tables, graphs, and equations reveal the structure of a function and its possible component functions?
  • Why is it useful to represent and analyze functions in multiple forms?
  • How can we determine whether a given function could be constructed by multiplying two or more simpler functions?
  • What patterns in different representations help us identify relationships among functions?