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Example 14 Two graphs are shown below Relate the function g x to f x...

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Geometry

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Example 14 Two graphs are shown below Relate the function g x to f x f x 5 4 3 2 g x 4 W 3 2 14 Show solution 6 to X Notice that the coefficient needed for a horizontal stretch or compression is the reciprocal of the stretch or compression To stretch the graph horizontally by 4 we need a coefficient This makes the inputs come in 1 4 as fast so the function takes 4 times longer to increase and decrease of 1 4 in our function 1 It is useful to note that for most toolkit functions a horizontal stretch or vertical stretch can be represented in other ways For example a horizontal compression of the function f x x by would result in a new function g x 2x but this can also be written as g x 4x a vertical stretch of f x by 4 When writing a formula for a transformed toolkit we only need to find one transformation that would produce the graph Exercise 1 5 7 Write a formula for the toolkit square root function f x x horizontally stretched by three

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