At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
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
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....