PreCalculus
Chapter 7 Rational Functions
Unit 7-1 Zeros, Vertical Asymptotes, and POEs
- Standard 7a: Find Zeros, Vertical Asymptotes, and Points of Exclusion of a Rational Function and distinguish them from one another
Agenda
- Three Unique Points in a Rational Function
- Zeros - where only the numerator is zero
- Vertical Asymptotes (VA) - where only the denominator is zero
- Points of Exclusion (POE) - where both are zero
- Assignment 7-1: Pg 438 #1-5, 8, 11
Unit 7-2 Sign Patterns of Rational Functions
- Standard 7b: Determine the end behavior of a rational function from a model, polynomial long division, or infinite limits and sketch the horizontal or slant asymptote.
Agenda
- Limits as x approaches ±∞
- Asymptotes
- Horizontal at 0
- Horizontal at a line other than 0
- Slant Asymptotes
- Assignment 7-2:
Pg 450 #1-4, 7-14, 16-22
Unit 7-3 End Behavior: Horizontal Asymptotes
- Standard 7c: Determine the end behavior or horizontal asymptote of a rational function from a model
- Standard 7d: Determine the end behavior or a rational function from long division
Agenda
- The Quotient Rule
- Sign Patterns of Rational Function Derivatives
- Finding Critical Points and Extreme Values Using the Quotient Rule
- Assignment 7-3: Part A Pg 461 #1-6 Part B Pg. 461 #10-11, 13, 14, 16, & 18
Unit 7-4 End Behavior: Slant Asymptotes
- Standard 7e: Use sign patterns to solve rational inequalities.
Agenda
- Review of Sign Patterns
- Denoting zeros, POE's, and vertical asymptotes on a number line
- Applying Sign Patterns to Rational Function Graphs
- Assignment 7-4: Part A Pg 468 #1-4 Part B #5-10
Unit 7-5 The Quotient Rule
- Standard 7f: Find the derivative of a rational function using the Quotient Rule
- Standard 7g: Apply sign patterns to the first derivative.
- Standard 7h: Find the extreme points of a rational function
Agenda
- The Quotient Rule
- Sign Patterns of Rational Function Derivatives
- Finding Critical Points and Extreme Values Using the Quotient Rule
- Assignment 7-5: Part A Pg. 479 #1-9 (can #4, 8, & 9 be done without the QR?)
Assignment 7-5: Part B Pg. 479 #10-11, 13, 14, 16, & 18 (#18 may require a calculator)
Unit 7-6 General Rational Curve Sketching
- Standard 7i: Use sign patterns to solve rational inequalities.
Agenda
- Review of Sign Patterns
- Denoting zeros, POE's, and vertical asymptotes on a number line
- Applying Sign Patterns to Rational Function Graphs
- Assignment 7-6: Part A Pg 390 #1-5 Part B #6-10
Unit 7-7 Sign Patterns of the Derivative of a Rational Function
- Standard 7j: Find all the traits and sketch a fairly accurate rational curve algebraically.
Agenda
- Review of Sign Patterns
- Denoting zeros, POE's, and vertical asymptotes on a number line
- Applying Sign Patterns to Rational Function Graphs
- Assignment 7-7: Pg. 407 # 1, 2, 3, 5, 6, 8, 13, 15, 17