Transformations of graphs
Competing phone companies
The functions represented in the tool below
describe the rates charged by two competing
cellular phone companies. Each company has
a fixed charge for each minute. One of the
companies also charges a basic monthly fee.
Each company wants to draw away customers
from its competitor by announcing a
rate reduction.
|
|
|
Use words to describe the rates of each of the companies.
| |
|
Describe the customers that will prefer one or the other company based on current rates.
|
|
The first company announced a special "free time" offer.
In the month of January, the company will offer 20 minutes of free time. (Customers who use the phone for
30 minutes during the month will pay only for 10 minutes.)
- Use the tool below to change the function describing
the rate of the first company so that it takes into account
the "free time" during January.
- What transformation needs to be performed on the graph
to describe the rate when a "free time" offer
is made during any month?
- What is the amount of free time you recommend
the first company to offer if it wants to attract all
the customers who use their cell phones for up to 5 hours
per month?
|
|
In reaction to the first company's "free time" offer, the second
company announced that it would reduce its basic monthly fee.
- What transformation needs to be performed on the graph to describe a reduction in the basic monthly fee?
- By how much should the second company reduce its basic
monthly fee in order to bring back the customers it lost
to the first company becuase of that company's "free time" offer?
|
|
|
How much will the customers of the two companies gain from the two reductions?
| |
|
|
|
| |
|
|
|
|
|
monthly bill (dollars) |
| minutes |
| |
| |
| |
| |
|
|
|
|
|
