Understanding a Simple Rational Function by Looking at a Graph and Table of Values

This lesson covers the creation of equations for simple rational functions using graphs and tables. It explains inverse proportionality, where one quantity increases as the other decreases, maintaining a constant product. A common mistake is forgetting this constant product. An example using parking costs illustrates the concept, showing how cost per person decreases as the number of people increases. The zero-product property is discussed, emphasizing that neither variable can be zero. The lesson concludes with a summary of these concepts.

What is a common mistake students make when dealing with simple rational functions?

• Forgetting that the product of variables is constant

• Assuming both variables increase together

• Believing the sum of variables is constant

• Thinking the variables are directly proportional

In the parking fee example, what happens to the cost per person as more people share the car?

• The cost per person doubles

• The cost per person increases

• The cost per person remains the same

• The cost per person decreases

What equation represents the relationship between the number of people and the cost per person in the parking fee example?

• p + m = 24

• p - m = 24

• p / m = 24

• p * m = 24

Why can't either variable in a simple rational function be zero?

• Because it would make the product infinite

• Because it would make the product undefined

• Because it would make the product zero

• Because it would make the product negative

What is the constant product in the parking fee example?

• $0

• $8

• $24

• $12