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This module provides practice problems designed to develop some concepts related to horizontal and vertical permutations of functions by graphing.
  1. In a certain magical bank, your money doubles every year. So if you start with $1, your money is represented by the function M = 2 t , where t is the time (in years) your money has been in the bank, and M is the amount of money (in dollars) you have.
    Don puts $1 into the bank at the very beginning ( t = 0 ).
    Susan also puts $1 into the bank when t = 0 . However, she also has a secret stash of $2 under her mattress at home. Of course, her $2 stash doesn’t grow: so at any given time t, she has the same amount of money that Don has, plus $2 more.
    Cheryl, like Don, starts with $1. But during the first year, she hides it under her mattress. After a year ( t = 1 ) she puts it into the bank, where it starts to accrue interest.
  1. Fill in the following table to show how much money each person has.
t=0 t=1 t=2 t=3
Don 1
Susan 3
Cheryl 1 1
  1. Graph each person’s money as a function of time.
  1. Below each graph, write the function that gives this person’s money as a function of time. Be sure your function correctly generates the points you gave above! (*For Cheryl, your function will not accurately represent her money between t = 0 and t = 1 , but it should accurately represent it thereafter.)
  1. The function y = f ( x ) is defined on the domain [–4,4] as shown below.
  1. What is f ( –2 ) ? (That is, what does this function give you if you give it a -2?)
  2. What is f ( 0 ) ?
  3. What is f ( 3 ) ?
  4. The function has three zeros. What are they?

The function g ( x ) is defined by the equation: g ( x ) = f ( x ) –1 . That is to say, for any x -value you put into g ( x ) , it first puts that value into f ( x ) , and then it subtracts 1 from the answer.

  1. What is g ( –2 ) ?
  2. What is g ( 0 ) ?
  3. What is g ( 3 ) ?
  4. Draw y = g ( x ) next to the f ( x ) drawing above.

The function h ( x ) is defined by the equation: h ( x ) = f ( x + 1 ) . That is to say, for any x -value you put into h ( x ) , it first adds 1 to that value, and then it puts the new x -value into f ( x ) .

  1. What is h ( –3 ) ?
  2. What is h ( –1 ) ?
  3. What is h ( 2 ) ?
  4. Draw y = h ( x ) next to the f ( x ) drawing to the right.
  1. Which of the two permutations above changed the domain of the function?
  1. On your calculator, graph the function Y 1 = x 3 13 x 12 . Graph it in a window with x going from –5 to 5, and y going from –30 to 30.
  1. Copy the graph below. Note the three zeros at x = –3 , x = –1 , and x = 4 .
y = x 3 13 x 12
  1. For what x-values is the function less than zero? (Or, to put it another way: solve the inequality x 3 13 x 12 < 0 .)
  2. Construct a function that looks exactly like this function, but moved up 10. Graph your new function on the calculator (as Y2, so you can see the two functions together). When you have a function that works, write your new function below.
  3. Construct a function that looks exactly like the original function, but moved 2 units to the left. When you have a function that works, write your new function below.
  4. Construct a function that looks exactly like the original function, but moved down 3 and 1 unit to the right. When you have a function that works, write your new function below.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Advanced algebra ii: activities and homework. OpenStax CNX. Sep 15, 2009 Download for free at http://cnx.org/content/col10686/1.5
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