1. Objective Define and illustrate the use of rational expressions and functions. 11.2 Rational Expressions and Functions Page 532 Rational Expressions and Functions

2. Glossary Terms rational expression hole (in a graph) non-trivial rational function rational function trivial rational function vertical asymptote

3. Rules and Properties Rational Expressions If P and Q are polynomials and Q  0, then is a rational expression. P Q 11.2 Rational Expressions and Functions

4. It is usually the case that you have to restrict values in the domain that give you a non-zero denominator. Whenever you have a value that makes the denominator zero, the function is undefined. At this value there is a ‘hole’ in the graph, or a vertical asymptote. A vertical asymptote is a vertical line that the graph approaches but never touches or crosses.

5. What is the domain of each of the following rational functions. List all restrictions. y = 1x1x Since the function is undefined at 0, the domain is all real numbers but 0. y = x² - 4 x - 2 Since the function is undefined at 2, the domain is all real numbers except 2. x ≠ 2 n = m – 2 m² - 5m + 6 m² - 5m + 6 = (m – 3)(m – 2) Since the function is undefined at 2 and 3, the domain is all real numbers except 2 and 3. x ≠ 2 and x ≠ 3

6. Key Skills Evaluate rational functions. List the values of the variable for which functions are undefined. 11.2 Rational Expressions and Functions undefined for x = 2 vertical asymptote at x = 2 f(x) = 4 x – 2 + 1 TOC

7. Assignment Page 536 –# 10 – 35, 36 – 44 even