9.1.3 Transforming Functions Key Objectives • Transform functions. • Recognize transformations of functions. Example 1 Transforming Piecewise Functions Piecewise functions can be transformed by applying transformations to each piece independently.
Example 2 Identifying Intercepts
When functions are transformed, the intercepts may or may not change. By identifying and examining the transformations, the intercepts can be determined, which can aid in graphing a transformed function.
Effects of Transformations on Intercepts of f ( x ) • Horizontal Stretch or Compression by a Factor of b x -intercepts are multiplied by b ; y -intercept stays the same • Vertical Stretch or Compression by a Factor of a x -intercepts stay the same; y -intercept is multiplied by a • Reflection Across the y -axis x -intercepts are multiplied by − 1; y -intercept stays the same • Reflection Across the x -axis x -intercepts stay the same; y -intercept is multiplied by − 1
248
Made with FlippingBook - Share PDF online