Curve Sketching
It is often said that ‘a picture is worth a thousand words’. In mathematics, it is often the case that the graph of a function is more useful than a table of values.
In the first two sections of this chapter, we develop techniques which allow us to sketch the graph of any rational function. The techniques include the location of critical points and points of inflection using differentiation. We will also look at what happens to the graph y = f(x) as x (or y) becomes large. This involves limits involving ∞, as discussed in Section 7.4. Most of the ideas apply to general functions, and some of the examples consider such cases.
Many plane curves are not the graph of a function. If we observe that a function takes a unique ...
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