Want to create interactive content? It’s easy in Genially!

Get started free

WEEK-15-REAL-LIFE-EXAMPLES-OF-RATIONAL-FUNCTIONS

VIMSCHOOL

Created on January 3, 2025

Start designing with a free template

Discover more than 1500 professional designs like these:

Microcourse: Team Cybersecurity

Microcourse: Learn Spanish

Retro Bits Quiz

Guess the Movies with Emojis

Movie Classics in Emojis

Movie Pairs

Movie Minigames

Explore all templates

Transcript

Real Life Examples of Rational Functions

Objectives

Start

Story

Key Concepts

Real-life examples

Summary

Story

Characters

Key Concepts

Rational function

A rational function is a function of the form:

where P(x) and Q(x) are polynomials and Q(x) .

Real-life examples

Example

A car travels 100 km. The time T(v) as a function of speed is modeled as:

Example number 2

A company that sells bottles of water sets its price according to the quantity available on the market. The relationship between the price 𝑃 and quantity π‘ž is modeled by the following equation:

  • π‘ž: number of bottles of water available in the market.
  • 𝑃(π‘ž): the price in pesos per bottle.

Try It By Yourself

Summary

Rational Functions

Great job!

See you next time

Welcome 6th graders!

A journey soon begin through Social Science experiences!

11TH-REAL-LIFE-EXAMPLES-OF-RATIONAL-FUNCTIONS-EN Β© 2025 by CASURID is licensed under CC BY-NC-ND 4.0

Vertical asymptotes: Values where the denominator cancels out, causing a discontinuity.

vertical asymptote

How to Solve them.

  • Substitute known values.
  • Factorize and simplify when possible.
  • Analyze constraints and behavior at extremes.

Analysis

  • In this case the number of products will always be positive.
25
23.8
22.7
21.7
20.8

MA.912.AR.8.3 Solve and graph mathematical and real-world problems that are modeled with rational functions. Interpret key features and determine constraints in terms of the context. MA.K12.MTR.7.1 Apply mathematics to real-world contexts. ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

According to the graph we can determine that:

  • The higher the speed, the shorter the time.
  • The lower the speed, the longer the time

How to Analyze Them

  • Domain: Allowable values for π‘₯
  • Asymptotes: Vertical (division by zero) and horizontal (limits).
  • Growth/Decrease: Trends of the function.
  • Intersections: Where it crosses the axes.

After graphing we can identify the following:

  • The higher the quantity of product, the lower the price of these products.

Analysis:

  • Velocity is not negative:
  • We cannot divide by zero.
  • We also know that time will never be 0.

Importance of Rational Functions

  • They model real-world phenomena.
  • They predict behaviors in economics, physics and engineering.
  • They help in decision making.