Sections, concepts, and problems

Section 1. The algebra of rational functions. Domains, roots, "holes", polynomial long division.
2, 4, 5, 13, 14, 15, 18, 24, 28, 30 - 35, 37, 39, 48

Section 2. Limits and asymptotes of rational functions. Limits at infinity and horizontal asymptotes, infinite limits and vertical asymptotes, other types of asymptotes.
5, 6, 12, 14, 16, 17, 19, 24-26, 36-38, 42, 43 (factor first), 52 (use long division to find the slant asymptote)

Section 3. Derivatives of rational functions. The quotient rule and extrema.
1, 2, 4 (easy: just look at the quotient rule), 17, 21, 24 (multiply out the bottom first), 32, 41 (note: same function as 32), 50 (just keep track of the degrees of the top and bottom ... if f=p/q, deg(p)=n, and deg(q)=m, then you know m>n ... use this to show the degree of the top of the derivative is less than the degree of the bottom of the derivative)

Section 4. Graphs of rational functions. Graphing rational functions roughly (without using its derivative and second derivative) and more accurately (using its derivative and second derivative).
2ab, 6, 9, 10, 14, 17 (note: I have only picked out the "rough sketch" type grapsh for fall 2004)

Other Chapters

Chap 0 | Chap 1 | Chap 2 | Chap 3 | Chap 4 | Chap 5 | Chap 6