Creating and Graphing Relationships Using Rational Functions

The video tutorial explores how to use rational functions to solve a cost-sharing problem, specifically renting a pool for $150. It explains rational functions as ratios of polynomials, their graphical representation, and common mistakes like input restrictions. The tutorial guides viewers through creating and graphing a function to determine the cost per person based on the number of people renting the pool. It highlights the concept of asymptotes and concludes with a summary of the lesson.

What is the primary focus of today's lesson?

• Understanding linear functions

• Learning about rational functions

• Exploring quadratic equations

• Studying exponential growth

Which of the following best describes a rational function?

• A polynomial and a constant

• Two polynomials divided by one another

• Two polynomials added together

• A single polynomial

What is a common mistake to avoid when working with rational functions?

• Ignoring the coefficients

• Mislabeling the axes

• Forgetting input restrictions

• Overlooking the constant term

What is the cost to rent the pool for a day?

• $250

• $150

• $200

• $100

How is the cost per person calculated in the pool rental problem?

• By dividing the total cost by the number of people

• By subtracting the number of people from the total cost

• By multiplying the total cost by the number of people

• By adding the total cost to the number of people

What happens to the cost per person as more people rent the pool?

• It remains constant

• It increases

• It decreases

• It becomes zero

What is a horizontal asymptote in the context of the pool rental problem?

• A point where the graph intersects the y-axis

• A line that the graph crosses at zero

• A point where the graph intersects the x-axis

• A line that the graph will never touch