Given a graph of y = f(x) how do you sketch a graph of y = f(x)+4, y = f(x-5), y = -f(x+4) or any other similar transformations

For y = f(x)+4: the graph undergoes a translation of (0,4) For y = f(x-5): the graph undergoes a translation of (5,0) For y = -f(x+4): the graph is reflected w.r.t the x-axis and translated by (-4,0)*imagine all translations as column vectors, I cannot work out how to type them like that.
For these questions getting the student to learn and also understand the rules and learn where they come from is key so in an exam they are able to figure them out for themselves. The method of using a set of x-values (e.g -2,-1,0,1,2) and putting them through both the original function and the altered one might be a good way to help students understand and would be good to teach as a back-up incase they forget when in an exam.