How to solve y=3f(x) and y=f(2x)

In this question we are given some unknown function, but we know that this unknown function has a minimum point at the coordinate 3,5. So it may look something like this: just a sketch of the graph. And the question is what happens to that minimum point for the following two transformations. Now three lots of f of x stretches the y coordinate by a factor of 3. So the y coordinate rather than being at 5, will be at 3 times 5 which is 15. But the x coordinate doesn't change.

So the new coordinate will be at still three across, but rather than 5 up it'll be 15 up. So 3,15 is the new coordinate of the min.point. Back to the graph here: f bracket 2x actually stretches the graph in the x direction but by a factor of not 2 but a half. So this is a stretch in the x direction factor ½. So the y coordinate doesn’t change, but the x coordinate gets a half. So 3 times ½ is 1.5 The 5 doesn't change, so the new coordinate is 1.5, 5.

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