Thank you for responding,a pilot on Facebook basically tried to explain the same thing to me the other day, your example is actually a little more clear, however I'm at a point where my lack of knowledge at understanding graphs is hindering me, and it's not reasonable for me to ask someone to interpret performance graphs everytime I need to interpret one. After looking for math study videos on YouTube I see there are many different graphs, what kind of graphs should I study that will allow me to have the necessary knowledge to interpret these kind of graphs?
This is not really a math issue; what is done here is not typical of any kind of graph you'd study in math. In particular, they don't tell you what the horizontal axis in the top graph means, so it wouldn't help much to try to use any knowledge from outside the graph.
They have attempted to
show how to use their graph, and any graph of this sort would include such instructions.
Words (such as in the screenshot you attached, which did help me to be more sure of my interpretation) would be at least a little more helpful than a couple cryptic arrows on the graph, but I wouldn't say I used any special mathematical skills to figure out what they meant.
I suppose one thing that might help you is some sort of experience with reading graphs "inside-out", which is done twice in this case:
Working backward from a y value to an x value using a curve. This can be described as "
solving for x graphically". The concept of
families of curves (which is what both graphs here show) might also help you get a feel for what these graphs mean (e.g. where we twice had to choose a curve intermediate between curves that are shown). So, yes, I guess there is some mathematical experience behind my success in understanding what they show.
One other thing: The style of usage of these graphs reminds me of
nomographs, which are specialize graphical representations of relationships in which you often draw lines between points on other lines to find an answer. That's not really what this is, but the way it's used involves some similar actions, and the goal (to quickly estimate a calculation) is the same. Possibly experience with them could help you. But nomographs are basically a technique that was used before computers, and they are rare these days.
Ultimately, though, it's going to be a matter of following instructions (in this case, a visual example), even when you don't initially know exactly what you're doing, and
then seeing whether it makes sense. When I teach problem-solving, I often recommend just
doing something as a step toward understanding.