posted by John on .
sketch the image of f(x) after:
a) a horizontal compression by a factor of 1/2
b) a veritcal expansion by a factor of 3
c) both transformations in parts a and c have been applied
d) write the equations of the three image for a b and c
i think i graphed a b and c right
but i cant seem to get the equations
i thought it was:
a) y = f(2x)
b) y = f(x-3)
c) y = f(2(x-3))
but the back of the book says
a)f(x) = (root(4-(2x-2)squared)
b) f(x) = (3(root(4-(x-2)squared)))
c) f(x) = (3(root(4-(2x-2)squared)))
I agree with you about (a). Part (b) is just y=3*f(x), and (c) is y=3*f(2x)). What you're describing in (b) is a translation of the function of 3 units to the right, not a vertical expansion of it by a factor of 3.
Having said all that, I can't see where the answers at the back of the book come from at all, unless either the function f(x) is some specific function that's given earlier in the question as opposed to a general f(x) that I think we're both assuming it is, or unless "the image of f(x)" means something other than just what f(x) is mapped onto. Does anyone else have any views on this?