Please enlighten me as to how graphing a function helps. I can see a graph's utility with simple functions as they instantly give you value of dependent variable. But ignoring them and considering three dimensional complex figures that often arise in higher level math, how does it help you solve the problem if you know that the graph is a knot or a doughnut or in 2D case say the 'U' shape of a parabola. I admire the wonderful shapes but I don't know what to make of them except having a visual treat. How do they help you solve a given problem?
Edit: Take the following graph as example. Some of you may recognize it but for others who don't what information does it convey to you in absence of any equation and how will it help you understand the physical phenomenon.
Please take me through your mental journey. I am desperate to see the world with same intuitiveness as any one of you do. Thanks again for your time