PLEASE SOMEONE HELP.
Functions are in the world all around us. You have used functions to model phenomena and to
make predictions. Mathematically, you can add, subtract, multiply, and divide functions, and you
can also create a composition of functions.
A composition of functions occurs when you evaluate one function using another function, or
even with the same function. A composition of functions is useful when a change in one function
will create a change in another function, which, in turn, affects a third function. For example,
suppose that humans build a housing development on land that was previously used as a corn
field. This change in land usage causes the number of birds in the area to decrease, which causes
the number of mosquitos to increase. You could model the increase in the number of mosquitoes
as a function of the number of birds in the area, which is a function of the number of humans that
live on that land.
You can also use the composition of functions to show that one function is the inverse of another
function. Recall that the graphs of inverse functions are reflections of each other over the line .
Think about these ideas as you read through the scenario below.
Last night it started raining as Hibah was closing up the store where she works. By 3 am, the roof
of the store developed a small hole and water began to leak onto the sales floor. The water
created a circular puddle on the floor. At any time, t,
in minutes, the radius of the puddle increases by 0.1
cm. The rain continued through the night, but stopped
by the time the morning shift arrived at the store at 7
am.
When the employees arrived at work, the leak and
water puddle were discovered. The employees
cleaned up the water puddle and placed a tall circular
bucket underneath the leak, which was still slowly
dripping. The capacity of the bucket can be expressed
as () = 83 + 42 − 6 + 5. By 10 am, the
amount of water in the bucket is () = 23 + 2 − 4 + 7.
Use the information given to explore some of the mathematical concepts you have practiced so
far by answering the questions below.