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why does f(2x) stretch horizontally by a scale factor of 1/2? why can't we just multiply the x values by 2?

Mathematics
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f(2x) stretches by 1/2 factor of f(x) horizontally because in the latter graph, you get the same range for rather half of the domain values
A function relates two numbers. For example the function f(x) = x takes x as input and provides x as the output. However a function f(2x) = x takes twice the value of x and plots it against x. Plotting the two functions should give you a feel for this.
you get the same graph if you multiply the domain values of x with 2 and plot it

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Other answers:

ok so for a while all of that made a lot of sense. but now i'm actually graphing and it's confusing again. so i graphed f(x) = x^2. now i'm doing f(2x). here does it become f(2x) = (2x) ^2?
y = 2x -> x= y/2
yes you are correct @joshi
ohhhh ok i get it now! it makes sense! thank you!
so whenever we'll have a f(2x) or f(3x) etc. question we'll just multiply all the x values of the coordinates by half? and so when we'll have f(1/2 x) we'll multiply the x values by 1/2/2 which is just 2? right?
http://www.wolframalpha.com/input/?i=y%3Dx^2%2C+y+%3D+4x^2%2C+y%3D+9x^2 These are graphs for x^2,4x^2 and 9x^2 which are what you would get for y=x^2 and then if for x you substituted 2x and 3x....

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