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Understanding Rational Functions and Horizontal Asymptotes: A Food-Themed Exploration

This lesson delves into rational functions using a food-themed mini-theme centered around fruits. It explores the conditions that determine horizontal asymptotes (HA) based on the degree of the numerator compared to the denominator. When the numerator degree is less than the denominator, the horizontal asymptote is ( y = 0 ). We also look into vertical asymptotes (VA) and how to graph these functions effectively. Real-world connections to food consumption, like starfruit and cherimoya, enrich the learning experience.

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Understanding Rational Functions and Horizontal Asymptotes: A Food-Themed Exploration

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  1. Lesson 23: Case 2 Rationals Mini-Theme: Food

  2. What makes a function Case 2? • Degree of the Numerator < Degree of the Denominator • End behavior approaches zero on both sides.

  3. What fruit is this? Starfruit!

  4. Horizontal Asymptotes • If Numerator Degree > Denominator Degree • There is NO HA • If Numerator Degree < Denominator Degree (Case 2) • Then HA: y=O • If Numerator Degree= Denominator Degree (Case 1) • HA = fraction of the leading coefficients • There are some cases when the HA will only exist at the far left and right. • This is based on the limits or end behavior

  5. Case of 2 or more VA’s • Example: Graph: • Need to find VA’s and zeros. Zero @ 2 HA: y=O • Do a sign chart to find out what the graph will look like. • HA only exist at the far right and left

  6. According to National Geographic: Which country leads the world in turkey consumption per capita? Israel Red meat is expensive there. Pork is not kosher

  7. Graph of:

  8. Steps to graph a Case 2: • Find the VA’s and HA’s • Find the zeros and y-int • Find the rest of the graph using the sign chart • Determine the sign on each side of the VA’s and zeros • Practice/Example: Graph and state the domain and range for:

  9. What fruit is this? • Cherimoya (or Moya) – has a taste that is a cross between a pineapple and a banana

  10. CFU

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