ALG1.MATH.3.E

Determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.

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

Standard Unwrapping

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Vocabulary
grapheffectsparent functionf(x) = xaf(x)f(x) + df(x - c)f(bx)valuesabcd
Skills
  • determine (effects of changing parameters a, b, c, and d in linear functions) #dok2
  • describe (the transformation of the parent function f(x) = x with various parameters) #dok2
  • compare (graphs before and after transformations to identify changes) #dok2
  • analyze (the impact on slope, y-intercept, and overall shape from parameter changes) #dok3
Learning Targets
  • I can identify the parent function f(x) = x and its graph. #dok1
  • I can state what the parameters a, b, c, and d represent in a transformed linear function. #dok1
  • I can apply values to a, b, c, and d to write new functions based on the parent function. #dok2
  • I can describe how changing a, b, c, and d affects the graph of f(x) = x. #dok2
  • I can predict how a transformation will shift, stretch, compress, or reflect the graph. #dok2
  • I can analyze graphs to determine which parameter changes caused specific transformations. #dok3
  • I can justify why a given transformation produces specific effects on the graph. #dok3
Big Ideas
  • Altering the parameters of a parent function allows us to generate all linear functions through transformations.
  • Understanding how each parameter affects a graph provides a foundation for modeling and interpreting real-world situations.
Essential Questions
  • How do changes to the parameters a, b, c, and d in f(x) transform the graph of the parent function?
  • What does each parameter (a, b, c, d) do to the parent function’s graph?
  • How can you predict the appearance of a graph after applying specific transformations?
  • Why is it important to understand how functions are transformed?
  • How do real-world contexts relate to graph transformations of the parent function?