ALG2.MATH.6.A

Analyze the effect on the graphs of f(x) = x3 and f(x) = 3√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
graphsfunctionf(x) = x^3f(x) = 3√xaf(x)f(bx)f(x - c)f(x) + dpositive real valuesnegative real valuesparameters a, b, c, deffect
Skills
  • analyze (the effect of transformations on the graphs of cubic and cube root functions) #dok2
  • describe (how changing parameters a, b, c, or d affect the graph of f(x) = x^3 and f(x) = 3√x) #dok2
  • identify (the type of transformation represented by af(x), f(bx), f(x-c), and f(x)+d) #dok1
  • compare (the original function and its transformed version) #dok2
Learning Targets
  • I can identify the parent graphs of f(x) = x^3 and f(x) = 3√x. #dok1
  • I can describe what each transformation parameter (a, b, c, d) does to cubic and cube root functions. #dok2
  • I can analyze the effect of multiplying by a positive or negative a on the graph. #dok2
  • I can analyze the effect of multiplying the input by b (positive or negative) on the graph. #dok2
  • I can analyze the effect of horizontal shifts (x-c) and vertical shifts (+d) on the graph. #dok2
  • I can compare the graphs of transformed functions with their parent functions. #dok2
  • I can predict the resulting graph given specific values for a, b, c, and d. #dok3
Big Ideas
  • Transformations change the appearance and position of a function's graph without altering its fundamental shape.
  • Understanding how parameters affect the graph of a function allows for modeling and interpreting real-world situations.
Essential Questions
  • How does changing each parameter (a, b, c, d) transform the graph of a cubic or cube root function?
  • What do positive and negative values for a, b, c, and d mean for the graph's orientation and position?
  • In what ways are cubic and cube root transformations similar and different?
  • How can I use transformations to model different scenarios using cubic and cube root functions?
  • How can I predict and describe the outcome of multiple transformations applied to these functions?