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    What is the reasoning behind the x being stretch by a factor of 1/2 rather than a factor of 2 ?, since it is 2x , which is rather counter intuitive.
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    (Original post by Bilbao)
    What is the reasoning behind the x being stretch by a factor of 1/2 rather than a factor of 2 ?, since it is 2x , which is rather counter intuitive.
    An example to get you thinking:

    f(x) = 2x

    f(2x) = g(x) = 2(2x)

    f(1) = 2
    g(0.5) = 2

    f(2) = 4
    g(1) = 4

    So to get to the same output in g as you do in f, you need to halve the input.
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    I struggled with this for a bit but recently got it

    Say you have the function y = f(x). It goes through the point (2, 4). You also have y = f(2x). Where does the point (2, 4) move to on the new graph? Well you know if you put in 2 into the function you will receive 4 as a value of y. So now you can "solve" for the new X coordinate: 2x = 2, so x = 2/2 = 1. From this it's very intuitive to see why you stretch by 1/2. Think of it as solving an equation.
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    (Original post by Bilbao)
    What is the reasoning behind the x being stretch by a factor of 1/2 rather than a factor of 2 ?, since it is 2x , which is rather counter intuitive.
    It is counter intuitive, yes, but then again there are plenty of other things in maths which are counter intuitive.

    Take a function y=f(x) which takes on a certain y value when x=X. Then introduce a transformation y=f(2x). We want to retain the exact same y value as the previous one, so we need to set 2x=X which hence means that x=\frac{X}{2}. Hence the new input into your transformed function is HALF the original one, and this applies to all x hence we say f(x) \mapsto f(2x) is a stretch by a factor 1/2 parallel to the x-axis.

    Same thing works when you transform y=f(x) to 2y=f(x). You half every y value, but more often you would rewrite the second eq. by saying that y=\frac{1}{2}f(x) and hence it is much more obvious to say that y halves, and so y \mapsto 2y is a transformation of a stretch factor 1/2 parallel to the y-axis.
 
 
 
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