how to sketch a funtion f(x)

1 find the domain of the function (where it exist) 2 find the solutions of the function, solve f(x)=0 3 if it has vertical asyntotes (poles) identify them (eg the denomitator=0) 4 find the intesections with the axis. Solve f(x)=0 (already done in point 2) and f(0)=? 5 do the limit of f(x) to see if the function has horizontal asintotes 6 take the first and second derivative to identify local maxima and minima 7 f(x)>0 can be solved to find where the function is positive and where it is negative Sketching all the identified features on a cartesian plane it is now easy to draw the function