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Section 1.6 Reflections, Absolute Values, and Other Transformations

Section 1.6 Reflections, Absolute Values, and Other Transformations. Box of Chocolates. Reflections across the x -axis and y -axis. Example 1. Write an equation for the reflection of this pre-image function across the y -axis.

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Section 1.6 Reflections, Absolute Values, and Other Transformations

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  1. Section 1.6 Reflections, Absolute Values, and Other Transformations

  2. Box of Chocolates

  3. Reflections across the x-axis and y-axis Example 1 Write an equation for the reflection of this pre-image function across the y-axis. Write an equation for the reflection of this pre-image function across the x-axis. Plot the pre-image and the two reflections on the same screen.

  4. Property: Reflections Across the Coordinate Axes is a vertical reflection of function f across the x-axis. is a horizontal reflection of function f across the y-axis.

  5. Absolute Value Transformations

  6. Piecewise function: A function follows different rules for different domains.

  7. Property: Absolute Value Transformations The transformation Reflects f across the x-axis if is nonnegative. Leaves f unchanged if is negative The transformation Leaves f unchanged for nonnegative values of x. Reflects the part of the graph for positive values of x to the corresponding negative values of x. Eliminates the part of f for negative values of x.

  8. Even Functions and Odd Functions (all odd exponents) (all even exponents)

  9. Definition: Even Function and Odd Function The function f is an even function if and only if for all x in the domain. The function f is an odd function if and only if for all x in the domain. Note: For odd functions, reflection across the y-axis gives the same image as reflection across the x-axis. For even functions, reflection across the y-axis is the same as the pre-image. Most functions do not possess the property of oddness or evenness.

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