Sketch the graph of a function f that satisfies all of the following conditions.

Question

 Please include these following conditions in the graph.

Answer 1

The graph looks something like this. The tiny circles at (-1,3), (-1,-2) and at x=4 show discontinuities (non-existent points of f(x)). The green broken lines are horizontal and vertical asymptotes. The red curves represent f(x), showing how they meet up with the discontinuities. f(x) approaches, but never touches, the asymptotes. Note that the discontinuity at x=4 has an arbitrary f(x) value (not necessarily what is shown).