PRECAL.MATH.2.G

Graph functions, including exponential, logarithmic, sine, cosine, rational, polynomial, and power functions and their transformations, including af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d, in mathematical and real-world problems.

Precalculus · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012

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Vocabulary
functionexponential functionlogarithmic functionsine functioncosine functionrational functionpolynomial functionpower functiontransformationsaf(x)f(x) + df(x - c)f(bx)values of a, b, c, and dmathematical problemsreal-world problems
Skills
  • graph (exponential, logarithmic, sine, cosine, rational, polynomial, and power functions) #dok2
  • apply (transformations to functions, such as af(x), f(x) + d, f(x - c), f(bx)) #dok2
  • interpret (the effects of specific transformations on the functions) #dok2
  • model (real-world and mathematical problems using transformed functions) #dok3
  • analyze (the purpose and effects of transforming functions in context) #dok3
Learning Targets
  • I can graph exponential, logarithmic, sine, cosine, rational, polynomial, and power functions. #dok2
  • I can apply specific transformations (af(x), f(x) + d, f(x - c), f(bx)) to functions. #dok2
  • I can identify the effects of each parameter (a, b, c, d) on the graph of a function. #dok2
  • I can interpret how a function's graph changes with transformations in mathematical and real-world contexts. #dok3
  • I can model real-world situations using transformed functions. #dok3
  • I can analyze how transformations affect the shape and position of a function's graph. #dok3
Big Ideas
  • Transformations allow us to modify and adapt basic functions to fit a wide variety of mathematical and real-world situations.
  • Understanding function transformations helps us interpret and predict the effects of changing parameters on graphs.
Essential Questions
  • How do changes in parameters a, b, c, and d affect the graph of a function?
  • What real-life situations can be modeled by transforming basic functions?
  • Why is it important to understand the impact of function transformations?
  • How can you determine which transformation has occurred by observing a graph?
  • How do different types of functions respond to the same transformation?