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 dimesional 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 the problem?
