translations of functions?

Question

What is the difference between the translations y=kf(x) and y=f(kx)

Answer 1

Neither of those is a translation.
A translation moves the graph up, down, left, right or some combination of these without changing the shape of the graph.

The functions that you gave are scaling functions.
y = kf(x) stretches (or shrinks) the graph in the y direction
y = f(kx) stretches (or shrinks) the graph in the x direction.

Edit: Also a negative k will reflect the graph about the x-axis or y-axis as well as stretch or shink it.

Answer 2

y=kf(x) means that you are working out f(x) first then multiplying by k. So you are changing the scale of the graph on the y-axis. For example if k were 2, the graph would be twice as high as normal.

Conversely, with y=f(kx) you are multiplying x first then evaluating the function. You are changing the rate at which the function's variable increases. That is, you are changing the scale on the x-axis. For example if k were 2 again, the function would squash horizontally to half its original width.

Answer 3

y=kf(x) starches or shrinks in the y
with y=f(kx) stretches or shrinks in the x
put it in a calc test it out. and solve it to your self, so look at it put numbers in it and figure it out but it should prob be (x)2 not just (x) cuz a with change would not effect a diagonal line. well the varies on the x or y, it only effect for like squared or square root.