Objective

• Define and illustrate the use of rational expressions and functions.

11.2 Rational Expressions and Functions

Page 532Rational Expressions and Functions

Glossary Terms

rational expressionhole (in a graph)non-trivial rational functionrational functiontrivial rational functionvertical asymptote

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

• 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.

What is the domain of each of the following rational functions. List all

restrictions.

y = 1x

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

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 asymptoteat x = 2

f(x) =4

x – 2+ 1

TOC

Assignment

• Page 536– # 10 – 35, 36 – 44 even