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2.7 Function Transformations and Compositions

Applying translations, reflections, stretches, and compositions to transform function graphs.

本节包含的知识点

  • 2.7.1 Vertical and Horizontal Translations — Understanding how adding or subtracting constants shifts function graphs vertically and horizontally.
  • 2.7.2 Reflections Across Axes — Analyzing how negating function values or inputs creates reflections across the x-axis and y-axis.
  • 2.7.3 Vertical and Horizontal Stretches/Compressions — Determining how multiplying functions by constants causes vertical stretching or compression and horizontal scaling.
  • 2.7.4 Combined Transformations — Applying multiple transformations sequentially to create complex function graphs with correct order of operations.
  • 2.7.5 Function Composition — Understanding how to combine functions through composition (f∘g) and analyzing the domain and range of composite functions.
  • 2.7.6 Inverse Functions and Transformations — Recognizing that inverse functions represent reflections across y=x and applying transformations to inverse relationships.