One must always keep in mind that computers plot a discrete set of points and make assumptions about the function's behaviour between these points.
Thus, caution is advisable with curve sketching.
We need the methods of calculus to analyze \(f(x)\) first and to generate a sketch of \(y=f(x)\) which accurately portrays the essential qualitative features of \(f\).
This process will be the focus of this unit.
Then, if needed, we can confidently use computers to generate quantitative information, knowing the relevant intervals of \(x\) and \(y\) and the points where special care is needed.