Graph Rational Functions Chapter 8-2, 8-3 Dr. Guram Algebra II

Focus Questions How will we graph rational functions with higher degree polynomials? How do we utilize rational functions in the real world?

Curriculum standards TN 3103.3.5 (Associated Tennessee Learning Expectations) Also: 3103.3.2, 3103.3.4, 3103.3.11, 3103.3.10 Describe the domain and range of functions and articulate restrictions imposed either by the operations or by the contextual situations which the functions represent. Sources: http://www.corestandards.org/Math/Content/HSA/CED/A/1/ Spring Board Algebra 2 Textbook

Real World Examples Utilizing Rational Functions What are examples of ways people utilize rational functions in real world situations? ???

Real World Example of Rational Functions Finding average monthly costs Solve problems about altitude

Asymptote: A line that a graph approaches more and more closely. Academic Language Rational function: A function of the form f(x) = p(x) / q(x), where p(x) and q(x) are polynomials and q(x) not equal 0. Asymptote: A line that a graph approaches more and more closely.

Academic Language End behavior: The behavior of the graph of a function as x approaches positive infinity, or negative infinity.

Parent Function for Simple Rational Functions

Example 1

Example 1

Graphing Translations of Simple Rational Functions

Example 2

Example 2

Guided Practice

Other Rational Functions

Example 3

Example 3

Guided Practice

Graphing Calculator

Graph of Rational Functions

Example 4

Example 4

Example 5

Example 5

Example 6

Example 6

Guided Practice

Review How will we graph rational functions with higher degree polynomials? How do we utilize rational functions in the real world?

Explain the mathematical terms: Review of terms Explain the mathematical terms: Rational Function Asymptote End behavior

Class and HW Problems Worksheet