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.