How do you sketch the graph of a function?

To sketch a graph, you can follow the steps below, spiking some of them if not needed or not applicable:0 Clean up the function (makes following steps easier).1 Determine the maximum domain of definition of the function if not given.2 Find out intersections of the graph with the axis if possible (optional).3 Find out if the function is odd or even or if it has periodicity. If it does, you can look at either one half(if even or odd) or only at a period (if periodical).4 Find out asymptotes and discontinuities5 Study the first derivative of the function6 Study the second derivative of the function6'If you can't determine the values that you need for the second derivative you may need to do the third derivative7 Do the variation table8 Sketch the graphSome steps can be skipped, depending on what is the purpose of sketching the graph. If the goal is to sketch the graph, to be more accurate all steps should be gone trough. If you want the extreme points you can only follow steps 0 1 3 4 5 and 7 .