Question

Can someone explain to me how I am supposed to know if there's a translation in the x or y direction...? For example: Given that (-3,-4) is on the graph of f(x), find the corresponding point for f(-3/4x).

Answer 1

for the same value of x, say for the point (-3,-4), x remains -3, but your y value is determined by the value of the function f, so even though you plug in x=-3 into the function f(-3/4x) you actually get the value of f((-3/4)*-3)) which is
f(9/4).So here for a value of x=-3 the y value is no longer f(-3)
but f(9/4)

Answer 2

But... how do I know which translation it is..? There's something I am just not grasping :(