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Mathematics - Algebra - Transforming Graphs

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I understand that when you transform y = f(x) to y = f(ax) it is a stretch in the x direction of scale factor 1/a, but I can't find any reasoning as to why the scale factor is 1/a and not just a. Can you explain?

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The expert examines transforming graphs. A complete, neat and step-by-step solution is provided.

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First of all, please note that when the graph of y = f(x) is transformed to y = f(ax), it is the dimension along the y- axis that

stretches or flattend and not the dimension along the x- axis.

For simplicity, let us take y = f(x) = x^2 [Blue ...

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