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Section 1-5

Section 1-5. Graphical Transformations. Section 1-5. vertical and horizontal translations reflections across the axes vertical and horizontal stretches and shrinks combining transformations. Vertical and Horizontal Translations. horizontal translations

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Section 1-5

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  1. Section 1-5 Graphical Transformations

  2. Section 1-5 • vertical and horizontal translations • reflections across the axes • vertical and horizontal stretches and shrinks • combining transformations

  3. Vertical and Horizontal Translations • horizontal translations • y = f (x – c) shifts right by c units examples: • y = f (x + c) shifts left by c units examples:

  4. Vertical and Horizontal Translations • vertical translations • y = f (x ) – c shifts down by c units examples: • y = f (x) + c shifts up by c units examples:

  5. Reflections Across Axes • reflection across the x-axis: y = – f (x) examples: • reflection across the y-axis: y = f (– x) examples:

  6. Vertical Stretches and Shrinks • a vertical stretch makes the graph narrower • a vertical shrink makes the graph wider • vertical stretch/shrink: • examples:

  7. Horizontal Stretches and Shrinks • a horizontal stretch makes the graph wider • a horizontal shrink makes the graph narrower • horizontal stretch/shrink: • examples:

  8. Combining Transformations • the order makes a difference • reflections are always applied first, but sometimes it is easier to sketch the graph by ignoring the reflection until the end • shift the graph into the correct position and then when you sketch it, make it narrower/wider and with any reflections

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