would it be safe to conclude that the transformation f(x/m) and mf(x) produce graphs that are identical? explain ur answer
Ummm, let us see.
f(x/m), mf(x)
I assume m is a constant.
mf(x) is m"f(x), I assume also.
f(x/m) and m*f(x) have identical graphs?
Say, m=3
And f(x/m) = f(x/3) = x^2 +2x + 6 ----(i)
What would be f(x)?
x = 3(x/3)
How are we generate the f(x)?
f(x) = (3x)^2 +2(3x) +6
f(x) = 9x^2 +6x +6 -----------(ii)
Check,
If f(x) = 9x^2 +6x +6, what is f(x/3)?
f(x/3) = 9(x/3)^2 +6(x/3) +6
f(x/3) = 9[ x^2 / 9] +2x +6
f(x/3) = x^2 +2x +6 -------same as (i).
So (ii) is okay. f(x) = 9x^2 +6x +6 ---------***
Now,
f(x/m) = f(x/3) = x^2 +2x +6 ---------(i)
mf(x) = m*f(x) = 3*f(x) = 3(9x^2 +6x +6) = 27x^2 +18x +18 ----(iii)
Would (i) and (iii) have identical graphs?
No. -----------answer.