How can you determine the relationship between two

numbers when the product is constant?

In this lesson you will learn how to create an equation for a

simple rational function by using a graph and a table of

values.

Let’s Review

A simple rational function: quantities are inversely proportional: As one

quantity gets larger, the other gets smaller

But the product remains constantxy = 12 or y = 12/x

A Common Mistake

Forgetting that the product of the two variables is constant

Core Lesson

How do we pay for parking when there is a flat rate of $24 per car?

People in Car

Amount paid per person

1 $24

2 $12

3 $8

4 $6

5 $4.80

6 $4 people

Cost per person

What happens to the cost per

person?

p x m = 24

Core Lesson

p x m = 24

Can either p or m ever be 0?

In this lesson you have learned how to create an equation for a

simple rational function by using a graph and a table of

values..

Guided Practice

The length of a playground is inversely proportional to its width. The area of the playground is 36 square feet. Determine the possible widths of the playground when the length is less than 5 feet.

Extension Activities

A concrete mixer can hold 60 cubic feet of concrete to pour onto a playground. The area that the concrete will cover is inversely proportional to the depth of the concrete poured, but the concrete must be at least 2 feet deep to hold the playground equipment. Make at least 3 different sketches for the shape and size of the playground.

Extension Activities

Find the possible perimeters for a rectangular playground whose area must be 120 square feet. What is the relationship between the perimeter and the area?

Quick Quiz

When gel is poured into a circular petri dish, the depth of the gel is inversely proportional to the square of the radius. Write an equation to show this relationship.

Quick Quiz

A school spends $7500 each year on student dances. The amount spent per dance depends upon how many dances are held. Write the equation of a function that models the relationship between the number of dances held and the cost of each.