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1.5b Combining Transformations

Learn how to apply a sequence of transformations to produce a graph of a given function and understand the importance of order in transformations. Practice problems included.

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1.5b Combining Transformations

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  1. 1.5b CombiningTransformations

  2. Let’s start with a problem: Describe a basic graph and a sequence of transformations that can be used to produce a graph of the given function. 2 Starting with y = x , • Does the order with which we apply these transformations matter??? translate right 3 units, vertically stretch by 2, and translate down 4 units.

  3. Combining Transformations Apply the following transformations, in order, to the graph of the squaring function. Graph the result. • a horizontal shift 2 units to the right • a vertical stretch by a factor of 3 • a vertical translation 5 units up Expand the final result!!!

  4. Combining Transformations Apply the following transformations, in order, to the graph of the squaring function. Graph the result. • a horizontal shift 2 units to the right • a vertical stretch by a factor of 3 • a vertical translation 5 units up Now, apply the same transformations, but in the opposite order. Expand the final result!!! The Moral: Order often matters when stretches, shrinks, or reflections are involved…

  5. More Practice Describe a basic graph and a sequence of transformations that can be used to produce a graph of the given function. 3 Starting with y = x , horizontally shrink by 1/3 and translate up 2 units.

  6. More Practice The graph of y = f(x) is shown. Determine the graph of the given composite function by showing the effect of a sequence of transformations on the graph of y = f(x).

  7. More Practice The graph of y = f(x) is shown. Determine the graph of the given composite function by showing the effect of a sequence of transformations on the graph of y = f(x). A vertical stretch by a factor of 2

  8. More Practice The graph of y = f(x) is shown. Determine the graph of the given composite function by showing the effect of a sequence of transformations on the graph of y = f(x). A horizontal translation 1 unit to the left

  9. More Practice The graph of y = f(x) is shown. Determine the graph of the given composite function by showing the effect of a sequence of transformations on the graph of y = f(x). A vertical translation 3 units down

  10. White board… Describe the translations to vertical shrink of ¼ horizontal shrink of 1/3, shift down 4 shift 2 left, reflection across y- axis, horizontal shrink of ¼, vertical shrink of ½, shift 3 up Homework: p. 140 29, 31, 35-49 Quiz tomorrow sections 1.4-1.5!

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