ALG2.MATH.4.C

Determine the effect on the graph of f(x) = √x when f(x) is replaced by af(x), f(x) + d, f(bx), and f(x - c) for specific positive and negative 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
graphquadratic functionsquare root functionf(x)af(x)f(x) + df(bx)f(x - c)positive and negative valuesabcd
Skills
  • identify (the effect of parameters a, b, c, and d on the graph of f(x) = √x) #dok1
  • determine (the impact of positive and negative values on the graph transformations) #dok2
  • analyze (graphical changes resulting from parameter modifications) #dok2
  • describe (how transformations like stretching, translating, or reflecting affect the square root function) #dok2
Learning Targets
  • I can identify the graph of f(x) = √x. #dok1
  • I can recognize a transformed square root function equation. #dok1
  • I can determine the effect of af(x) on the graph of f(x) = √x for positive and negative values of a. #dok2
  • I can analyze how the graph changes when f(x) = √x is transformed by f(bx) for different b values. #dok2
  • I can describe how f(x) + d translates the graph of f(x) = √x up or down. #dok2
  • I can analyze how the graph of f(x) = √x is shifted left or right by f(x - c). #dok2
  • I can create and interpret transformed square root graphs in context. #dok3
  • I can justify the impact of different parameter values and predict the resulting graph. #dok3
Big Ideas
  • Transformations such as stretching, compressing, reflecting, and translating change the appearance and position of the square root function on a graph.
  • Changing the parameters a, b, c, and d in the function f(x) = √x affects its graph in predictable ways, which students can systematically analyze and apply.
Essential Questions
  • How does changing each parameter (a, b, c, or d) affect the graph of f(x) = √x?
  • What patterns can you observe in the graph after applying a transformation?
  • How can understanding transformations help you graph and interpret real-world situations?
  • What is the difference between horizontal and vertical transformations of f(x) = √x?
  • How do positive and negative values of each parameter change the shape or direction of the graph?