suppose that the x-intercepts of the graph of y=f(x) are 2 and 3. What are the x-intercepts of y=f(x-6)
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Let y=f(x) be the same as f(x)=(x-2)(x-3)g(x), where g is another function of x. The given zeroes (i.e., the x intercepts) satisfy f(x)=0. If we replace x with x-6 we get f(x-6)=(x-8)(x-9)g(x-6), so the zeroes are 8 and 9, the x intercepts.

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