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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. One way of expressing a function is with a table. The following table defines the function f ( x ) .
x 0 1 2 3
f ( x ) 1 2 4 8
  1. f ( 2 ) =
  2. f ( 3 ) =
  3. f ( 4 ) =

Now, I’m going to define a new function this way: g ( x ) = f ( x ) −2 . Think of this as a set of instructions, as follows: Whatever number you are given, plug that number into f ( x ) , and then subtract two from the answer.

  1. g ( 2 ) =
  2. g ( 3 ) =
  3. g ( 4 ) =

Now, I’m going to define yet another function: h ( x ) = f ( x 2 ) . Think of this as a set of instructions, as follows: Whatever number you are given, subtract two. Then, plug that number into f ( x ) .

  1. h(2)=
  2. h(3)=
  3. h(4)=
  4. Graph all three functions below. Label them clearly so I can tell which is which!
  1. Standing at the edge of the Bottomless Pit of Despair, you kick a rock off the ledge and it falls into the pit. The height of the rock is given by the function h ( t ) = –16 t 2 , where t is the time since you dropped the rock, and h is the height of the rock.
  1. Fill in the following table.
time (seconds) 0 ½ 1 2 3
height (feet)
  1. h ( 0 ) = 0 . What does that tell us about the rock?
  2. All the other heights are negative: what does that tell us about the rock?
  3. Graph the function h ( t ) . Be sure to carefully label your axes!
h ( t ) = 16 t 2
  1. Another rock was dropped at the exact same time as the first rock; but instead of being kicked from the ground, it was dropped from your hand, 3 feet up. So, as they fall, the second rock is always three feet higher than the first rock.
  1. Fill in the following table for the second rock.
time (seconds) 0 ½ 1 2 3
height (feet)
  1. Graph the function h ( t ) for the new rock. Be sure to carefully label your axes!
  1. How does this new function h ( t ) compare to the old one? That is, if you put them side by side, what change would you see?
  2. The original function was h ( t ) = –16 t 2 . What is the new function?
    h ( t ) =
    (*make sure the function you write actually generates the points in your table!)
  3. Does this represent a horizontal permutation or a vertical permutation?
  4. Write a generalization based on this example, of the form: when you do such-and-such to a function, the graph changes in such-and-such a way.
  1. A third rock was dropped from the exact same place as the first rock (kicked off the ledge), but it was dropped 1½ seconds later, and began its fall (at h = 0 ) at that time.
  1. Fill in the following table for the third rock.
time (seconds) 0 ½ 1 2 3 4 5
height (feet) 0 0 0 0
  1. Graph the function h ( t ) for the new rock. Be sure to carefully label your axes!
  1. How does this new function h ( t ) compare to the original one? That is, if you put them side by side, what change would you see?
  2. The original function was h ( t ) = –16 t 2 . What is the new function?
    h ( t ) =
    (*make sure the function you write actually generates the points in your table!)
  3. Does this represent a horizontal permutation or a vertical permutation?

Write a generalization based on this example, of the form: when you do such-and-such to a function, the graph changes in such-and-such a way.

Questions & Answers

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..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
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
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.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
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
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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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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