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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

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
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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