In general:
\(f(x-a)\) shifts the function \(f(x)\) \(a\) units in the positive x direction
\(f\left(\frac{x}{a}\right)\) dilates the function \(f(x)\) horizontally by a factor of \(a\)
\(af(x)\) dilates the function \(f(x)\) vertically by a factor of \(a\)
\(f(x) + a\) shifts the function \(f(x) a\) units in the positive y direction
\(f(-x)\) reflects the function in the y-axis, while \(-f(x)\) reflects the function in the x-axis. In some way, you can technically consider them as a dilation in either the x or y direction.
Note for a sequence of changes that involves some combination of the above, order is very important.
For example, dilating a function \(f(x)\) by a factor of \(\frac{1}{2}\) then shifting it four units to the right will yield a different function than doing those steps in the reverse direction. A decent order to follow is shift in the x-direction, dilate in the x-direction, dilate in the y-direction, shift in the y-direction (though this may not be immediately helpful in some situations). Note also that reflection can technically be considered as 'dilation' given the way reflection works from the above tips, and as such can and should be applied in the same step. Working backwards may also be helpful.