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Pre-Cal

Pre-Cal. Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations. Definitions. Transformations : operations that change the location, orientation, or size of a graph.

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Pre-Cal

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  1. Pre-Cal Chapter 1 Functions and Graphs Section 1.5 Graphical Transformations

  2. Definitions • Transformations: operations that change the location, orientation, or size of a graph. • Rigid Transformations: this type of transformation does not change the size or shape of the graph. It can move the graph horizontally, vertically, or reflect the graph about a given line. • Non-Rigid Transformations: this type of transformation changes the shape of the graph. This could include stretching it horizontally and/or vertically.

  3. Definitions Cont. • Vertical Translation: this translation shifts the graph up or down in the coordinate plane. • Horizontal Translation: this translation shifts the graph to the left or right in the coordinate plane.

  4. Reflections • Reflections across the x-axis keep the same x value but switch the y values. So if your coordinate is (-2,4), when you reflect it about the x-axis, your new coordinate would be (-2,-4). • Reflections across the y-axis keep the y values the same but switch the x values. So if your coordinate is (4,-1), when you reflect it about the y-axis, your new coordinate would be (- 4,-1)

  5. Reflections Cont. • When you are completing the reflections for an actual graph of f(x) you need the follow the following rules: • Across the x-axis: y = -f(x) • Across the y-axis: y = f(-x)

  6. Stretches • When you multiply your coordinate by a number, then you are performing either a vertical shrink or stretch. Ie. y = c • f(x) • A shrink occurs when the number you are multiplying by is < 1. So c < 1 • A stretch occurs when the number you are multiplying by is > 1. So c > 1

  7. Stretches Cont. • A horizontal shift takes place when you are dividing the x by some number(c). So y = f(x/c) • A shrink occurs when c < 1. • A stretch occurs when c > 1.

  8. Translations • Given y = f(x) • Horizontal translations move the graph to the right or left using the following rules: • y = f(x-c) translates the graph c units to the right. • y = f(x+c) translates the graph c units to the left

  9. Translations Cont. • Vertical translations move the graph up or down using the following rules: • y = f(x) + c moves the graph up c units • y = f(x) – c moves the graph down c units

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