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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

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
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
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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
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
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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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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