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F(x)= x; translation 2 units right followed by a horizontal stretch by a factor of 2

User Gordon Guthrie
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1 Answer

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Final answer:

The transformed function f(x) = x after a translation of 2 units right and a horizontal stretch by a factor of 2 is h(x) = (x - 2)/2.

Step-by-step explanation:

The student is asking about transformations of the function f(x) = x. First, the function undergoes a translation 2 units to the right, which in mathematical terms is represented by the new function g(x) = f(x - 2). This effectively shifts the graph of f(x) 2 units to the right along the x-axis. Then, the function is horizontally stretched by a factor of 2, which means we take the input value and divide it by the stretch factor. The resulting function after this horizontal stretch is h(x) = g(x/2). Combining these two transformations, the final transformed function is h(x) = f((x - 2)/2) or simply h(x) = (x - 2)/2.

User Zentoaku
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