ALG2.MATH.6.G

Analyze the effect on the graphs of f(x) = 1/x when f(x) is replaced by af(x), f(bx), f(x-c), and f(x) + d for specific positive and negative real values of a, b, c, and d.

Algebra II · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

Standard Unwrapping

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Vocabulary
graphfunctionf(x) = 1/xaf(x)f(bx)f(x-c)f(x) + dpositive real valuesnegative real valuesabcd
Skills
  • analyze (changes to the graph of f(x) = 1/x from transformations) #dok3
  • recognize (effects of parameters a, b, c, d on the rational function graph) #dok2
  • apply (positive and negative real values to transformation rules) #dok2
  • identify (resulting transformations on the parent function f(x) = 1/x) #dok2
  • interpret (how each transformation affects aspects like asymptotes and symmetry) #dok3
Learning Targets
  • I can recall the general shape and properties of the function f(x) = 1/x. #dok1
  • I can define vertical and horizontal asymptotes for f(x) = 1/x. #dok1
  • I can list the effect of multiplying f(x) by a constant on its graph. #dok1
  • I can describe how the parameters a, b, c, and d transform the parent function f(x) = 1/x. #dok2
  • I can determine the effect of a transformation such as af(x), f(bx), f(x-c), or f(x)+d on the graph of f(x) = 1/x for any value of a, b, c, and d. #dok2
  • I can identify which transformations reflect, translate, or stretch/compress the graph of f(x) = 1/x. #dok2
  • I can analyze and explain the combined effect of multiple transformations applied to f(x) = 1/x. #dok3
  • I can explain how changes in a, b, c, and d affect the asymptotes and orientation of the function f(x) = 1/x. #dok3
  • I can evaluate a transformed rational function and predict its graph under different parameter changes. #dok3
Big Ideas
  • Transforming rational functions alters their graphs in predictable ways, affecting properties like asymptotes, orientation, and symmetry.
  • Understanding the effects of function transformations enables deeper insight into function behavior and algebraic modeling.
Essential Questions
  • How does changing each parameter (a, b, c, d) affect the graph of f(x) = 1/x?
  • What happens to the asymptotes and symmetry of f(x) = 1/x when transformed?
  • How can the rules of transformation help you predict the new graph without plotting points?
  • What is the impact of combining more than one transformation at a time on the graph of f(x) = 1/x?
  • How do these transformations connect to solving real-world problems modeled by rational functions?