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Graphical Transformations. Vertical and Horizontal Translations Vertical and Horizontal Stretches and Shrinks. Take the equation f(x)= x 2. How do you modify the equation to translate the graph of this equation 5 units to the right?........ 5 units to the left?

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## Graphical Transformations

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**Graphical Transformations**Vertical and Horizontal Translations Vertical and Horizontal Stretches and Shrinks**Take the equation f(x)= x2**• How do you modify the equation to translate the graph of this equation 5 units to the right?........ 5 units to the left? • How do you modify the equation to translate the graph of this equation 3 units down?..............3 units up? • What if you wanted to translate the graph of this equation 5 units to the left and 3 units down?**The parabola has been translated 5 units to the right.**How is the equation modified to cause this translation?**Notice the change in the equation y = x2 to create the**horizontal shift of 5 units to the right. f(x) = x2 g(x) = (x-5)2**The parabola is now translated 5 units to the left.**How is the equation modified to cause this translation?**Notice the change in the graph of the equation y=x2 to**create a horizontal shift of 5 units to the left. f(x)=x2 h(x)=(x+5)2**The parabola has now been translated three units down.**How is the equation modified to cause this translation?**Notice how the equation y = x2 has changed to make the**Vertical translation of 3 units down. f(x)=x2 q(x)=x2-3**The parabola has now been translated 3 units up.**How is the equation modified to cause this translation?**Notice how the equation y = x2 has been changed to make the**Vertical translation 3 units up. f(x)=x2 r(x)=x2+3**Write what you think would be the equation for translating**the parabola 5 units to the left and 3 units up?**The equation would be**What would the graph would look like?**g(x) is the translation of f(x) 5 units to the left and 3**units up. f(x)= x2 g(x) = (x+5)2+3**Vertical and horizontal stretches and shrinks**• How does the coefficient on the x2 term affect the graph of f(x) = x2? • What if we substitute an expression such as 2x into f(x)? How would that affect the graph of f(x) = x2?**The parabola has been vertically stretched by a factor of 2.**Notice how the equation has been modified to cause this stretch.**The parabola is vertically shrunk by a factor of ½.**Notice how the equation has been modified to cause this shrink.**By substituting an expression like 2x in for x in f(x) = x2**gives a different type of shrink. f(2x) = (2x)2. A horizontal shrink by a factor of ½.**Suppose we found g(1/2x). The equation would be**y = (1/2x)2.. How would this affect the graph of the function g(x) = x2? It is a horizontal stretch by a factor of 2.**If we were to write some rules for translations of functions**and stretches/shrinks of functions, what would we write? Horizontal translation: Vertical translation: Vertical stretch: Vertical shrink: Horizontal stretch: Horizontal shrink:

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