ALG2.MATH.6.C

Analyze the effect on the graphs of f(x) = |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

AI-generated as a starting point — sign in to edit.
Vocabulary
effectgraphsfunctionf(x) = |x|af(x)f(bx)f(x-c)f(x) + dvaluesabcd
Skills
  • analyze (effect of transformations on the graph of f(x) = |x|) #dok2
  • identify (how positive and negative values of a, b, c, d change the graph of f(x) = |x|) #dok1
  • describe (different types of transformations: vertical stretch/compression, horizontal stretch/compression, translation, reflection) #dok2
  • predict (the graphical result of applying transformations to f(x) = |x|) #dok2
Learning Targets
  • I can identify the parent graph of f(x) = |x|. #dok1
  • I can recognize transformation notation in equations of the form af(x), f(bx), f(x-c), and f(x) + d. #dok1
  • I can describe the effect of varying parameters a, b, c, and d on the graph of f(x) = |x|. #dok2
  • I can analyze how positive and negative values of a, b, c, and d change the shape and position of the absolute value graph. #dok2
  • I can predict the new graph when a transformation is applied to the absolute value function. #dok2
  • I can explain in my own words the impact of specific transformation parameters on the absolute value graph. #dok3
  • I can model and solve real-world problems involving transformed absolute value functions. #dok3
Big Ideas
  • Graphs of absolute value functions can be transformed through changes in the parameters a, b, c, and d, resulting in various shifts, stretches, compressions, and reflections.
  • Understanding how each parameter in the transformed function affects the graph allows for accurate interpretation and construction of absolute value functions to model diverse situations.
Essential Questions
  • How does each parameter (a, b, c, and d) change the shape or position of the graph of f(x) = |x|?
  • Why is it important to understand transformations of the absolute value function?
  • What real-life situations can be modeled using transformed absolute value functions?
  • How can you predict the outcome on the graph before actually graphing a transformed absolute value function?
  • How do multiple transformations applied at once affect the graph compared to a single transformation?