ALG2.MATH.5.A

Determine the effects on the key attributes on the graphs of f(x) = bx and f(x) = logb (x) where b is 2, 10, and e when f(x) is replaced by af(x), f(x) + d, and f(x - c) for specific positive and negative real values of a, c, and d.

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

Standard Unwrapping

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Vocabulary
key attributesgraphsfunctionf(x) = bxf(x) = logb(x)b (base)af(x)f(x) + df(x - c)real valuesacdpositive valuesnegative values
Skills
  • identify (key attributes of exponential and logarithmic functions) #dok1
  • describe (effects of transformations on exponential and logarithmic graphs) #dok2
  • analyze (changes in key attributes resulting from transformations) #dok3
  • compare (original and transformed graphs of exponential and logarithmic functions) #dok2
Learning Targets
  • I can identify the key attributes of f(x) = bx and f(x) = logb(x) where b is 2, 10, or e. #dok1
  • I can recognize the effect of multiplying, shifting, and translating exponential and logarithmic functions. #dok1
  • I can describe how changing a, c, and d in af(x), f(x + d), and f(x - c) affects the graph’s attributes. #dok2
  • I can compare graphs and explain the impact of positive or negative values for a, c, and d. #dok2
  • I can analyze the effects of multiple transformations (stretch, reflection, translation) on exponential and logarithmic graphs. #dok3
Big Ideas
  • The key attributes of exponential and logarithmic functions change in predictable ways under transformations.
  • Understanding how to manipulate parameters allows modeling and interpretation of real-world phenomena using exponential and logarithmic functions.
Essential Questions
  • How do changes to the parameters a, c, and d affect the graph of an exponential or logarithmic function?
  • What are the key attributes of exponential and logarithmic functions, and how are these attributes represented graphically?
  • How can understanding function transformations help in modeling real-world situations?
  • How can you predict the direction and magnitude of changes to the graph when a, c, or d is positive or negative?
  • Why is it important to recognize these changes when using exponential and logarithmic models?