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Mastering Function Transformations: Shifts, Reflections, and Stretches

Learn how to vertically and horizontally shift, reflect, and stretch functions effectively with positive and negative values. Understand the sum, difference, product, and quotient of functions.

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Mastering Function Transformations: Shifts, Reflections, and Stretches

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  1. 2.5 Transformations and Combinations of Functions

  2. Vertical Shift Up Y=f(x)+c Y=f(x)

  3. Vertical Shift Down Y=f(x) Y=f(x)-c

  4. Horizontal Shift to the Left Y=f(x+c) Y=f(x)

  5. Horizontal Shift to the Right Y=f(x) Y=f(x-c)

  6. Study Tip • We know that positive numbers are to the right of zero on a number line and negative numbers are to the left of zero. This positive-negative orientation does not apply to horizontal shifts. A positive number causes a shift to the left and a negative number causes a shift to the right.

  7. Reflection About the x-Axis Y=f(x) Y=-f(x)

  8. Reflection About the y-Axis Y=f(-x) Y=f(x)

  9. Vertical Stretching and Shrinking Graphs

  10. Vertical Stretching and Shrinking Graphs Y=f(x) Y=2f(x) Y=1/2f(x)

  11. Summary of Transformationsc represents a positive real number.

  12. Summary of Transformationsc represents a positive real number.

  13. Summary of Transformationsc represents a positive real number.

  14. Summary of Transformationsc represents a positive real number.

  15. Summary of Transformationsc represents a positive real number.

  16. The Sum of Functions

  17. The Difference of Functions

  18. The Product of Functions

  19. The Quotient of Functions

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