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

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AbhimanyuPudiBest ResponseYou've already chosen the best response.0
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
 one year ago

adonaisBest ResponseYou've already chosen the best response.0
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.
 one year ago

AbhimanyuPudiBest ResponseYou've already chosen the best response.0
you get the same graph if you multiply the domain values of x with 2 and plot it
 one year ago

joshiBest ResponseYou've already chosen the best response.0
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?
 one year ago

AbhimanyuPudiBest ResponseYou've already chosen the best response.0
yes you are correct @joshi
 one year ago

joshiBest ResponseYou've already chosen the best response.0
ohhhh ok i get it now! it makes sense! thank you!
 one year ago

joshiBest ResponseYou've already chosen the best response.0
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?
 one year ago

estudierBest ResponseYou've already chosen the best response.0
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....
 one year ago
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