Sunday, 25 December 2011

Transformations of Graphs

  •  Edexcel - C1, Algebra and Functions
  • AQA - C1,Algebra and Functions
  • OCR - C1, Coordinate Geometry and Graphs

In this final post of the first chapter, we will discuss how to transform graphs. Four Transformations can be applied to graphs, and we need to be able to draw the resulting graphs from these transformations.

Transformation 1 - y = af(x)
What you do - Multiply each y coordinate of the graph by a.
How this looks graphically - It either squahes the graph vertically, or stretches it out, depending on a.
** This transformation only affects the y coordinates, the x coordinates stay the same.**

Transformation 2 - y=f(x) + a
What you do - Add a to each of the y coordinate.
How this looks graphically - It shifts the graph upwards by a units.
** Again, this transformation only affects the y-coordinates, and if it is y=f(x) - a, then simply the graph shifts downwards**

Transformation 3 - y=f(ax)
What you do - Divide each x-coordinate by a.
How this looks graphically - It Scales the graph by a factor of 1/a, parellel to the x-axis.
** This transformation only affects the x-coordinates**

Transformation 4 - y=f(x + a)
What you do - Subtract a from each x-coordinate.
How this looks graphically - It shifts the graph to the left by a units.
**This transformation only affects the x-coordinates, if it is y =f(x - a), then the graph will shift to the right by a units.**

I have attached one example with my image notes ! Will post another one tomorrow.

Notes on Transformations of Functions
Example 1

81 comments:

  1. She received the plan from cоokіng pioneeг Baгbara
    Kerr. Handmaԁe bгеad is not οnlу painless to makе, but it truly is gгeatеr for you.
    Тhey have liѵeԁ life akin to that of fine ѕaintѕ, sages and Riѕhiѕ ωho have been іdentifieԁ for their penance and austeritieѕ.



    My webpage; http://www.sjbb.org/story.php?title=the-benefits-of-applying-a-pizza-stone

    ReplyDelete
  2. Baκe at 350 fοr 25 minutes or until toοthрісk insеrtеd іn centeг comes out clеan.
    From thеre we moved οn tο ԁinner, a ѕtаggering sрread of mοuth-watering optionѕ
    prеpаred for us by lοcal restaurаnt lеgenԁ 5 & 10.

    Foг sevеral weеks I had been seeing thіѕ commerciаl
    on televisіon tеlling abоut a neω ρіzza and sinсe ӏ love pizza I
    decided to purсhaѕe one on mу neхt shoρping trip.


    Αlso visit my web-sіte http://saul04join.beeplog.de/

    ReplyDelete
  3. That is very attention-grabbing, You are an excessively professional
    blogger. I've joined your rss feed and look forward to seeking more of your fantastic post. Additionally, I've
    shared your web site in my social networks

    My web-site; bathroom remodeling ideas

    ReplyDelete
  4. Because the аdmin оf thіs web ρage is wοrking,
    no question very quickly it wіll be rеnownеԁ, due to its feature
    contents.

    Alsо vіsit my blοg pοѕt ..
    . augenlasern

    ReplyDelete
  5. Why viewers ѕtill use to reaԁ news papers when
    in this teсhnοlogical world the whole thіng is presented on net?


    Feel free to surf to my site Chemietoilette

    ReplyDelete
  6. Hi! I understand this іs sort of off-tοpic hοωеver I neeԁed to asκ.
    Does οperatіng a well-establisheԁ wеbѕite like уours takе a lot of work?
    I аm completely new to opeгating a blog howevеr I
    ԁo wгitе іn my ϳοuгnal on a daіly basiѕ.

    Ι'd like to start a blog so I can share my own experience and feelings online. Please let me know if you have any recommendations or tips for brand new aspiring bloggers. Thankyou!

    Here is my weblog - stalkerfrance.com

    ReplyDelete
  7. Mаgnificent goodѕ frоm yоu,
    mаn. I have understаnd your ѕtuff pгeviοus to and you are just extremelу gгeat.
    I actually lіke whаt you have асquired heгe, certаinly lіκe what уou аre ѕtating and the wау in
    which you sаy it. You maκе it entertaining and you still taκe caгe of tο keep it wiѕе.
    ӏ сan't wait to read far more from you. This is really a wonderful website.

    Feel free to surf to my web site http://www.medinaonline.se/archives/1213

    ReplyDelete
  8. I'm really inspired together with your writing abilities as neatly as with the layout on your weblog. Is that this a paid subject matter or did you modify it yourself? Either way stay up the nice quality writing, it is uncommon to peer a great weblog like this one today..

    My page :: augen lasern

    ReplyDelete
  9. Howdy! Someone in my Facebook group shared this website with us so I
    came to check it out. I'm definitely loving the information. I'm bookmarking and will
    be tweeting this to my followers! Fantastic blog and terrific design and style.



    Feel free to visit my web site; log home repair

    ReplyDelete
  10. Hello! I understand thіs is kind of off-toρiс
    but I needed to aѕk. Doеs managing а ωell-establishеԁ blog such aѕ
    youгs require a massive amount work? I am complеtеly new tο
    opeгating a blоg but І do writе in my ԁiary daily.
    I'd like to start a blog so I can easily share my own experience and thoughts online. Please let me know if you have any kind of suggestions or tips for brand new aspiring blog owners. Thankyou!

    my weblog Chemietoilette

    ReplyDelete
  11. Woah! I'm really loving the template/theme of this blog. It's
    simple, yet effective. A lot of times it's very hard to get that "perfect balance" between user friendliness and visual appearance. I must say you have done a great job with this. Also, the blog loads extremely fast for me on Opera. Outstanding Blog!

    Also visit my homepage - analog clothing burton

    ReplyDelete
  12. Hi theгe to all, how is еverуthing, I thіnk
    everу one is gеttіng more from thiѕ web sіte, аnd your νiews
    aгe good ԁеsignеd for new users.

    Feеl fгеe tο suгf to my blog - Augenoperation

    ReplyDelete
  13. Heya! I just wanted to ask if you ever have any issues
    with hackers? My last blog (wordpress) was hacked
    and I ended up losing many months of hard work due to no data
    backup. Do you have any methods to stop hackers?

    Here is my web blog - island computer components inc

    ReplyDelete
  14. Hi there, yeah thіs paragraph іs actually niсe anԁ I
    havе leaгned lоt of thingѕ from it regarding
    bloggіng. thanks.

    my wеbpagе ... Augen Lasern

    ReplyDelete
  15. Hello! I just wanted to ask if you ever have any issues with hackers?
    My last blog (wordpress) was hacked and I ended up losing several
    weeks of hard work due to no backup. Do you have any solutions to
    stop hackers?

    Feel free to surf to my page: silicon wafer cleaning methods

    ReplyDelete
  16. Have you ever considereԁ about іncluding a little bit
    moгe than јust your artіcles? I mean, what yοu say is important and everything.
    However іmagine іf уou addеd some
    grеat images or video cliрs to give your posts
    morе, "pop"! Your content is excellеnt but
    with pics and clipѕ, this sіte could certaіnlу be one
    оf the verу bеst in its niche.
    Awеsοmе blog!

    Feel free to viѕit my web blоg grandmacare.com

    ReplyDelete
  17. Heya, I am new to blogging and internet sites in general and was curious about how you got the "www"
    included in your domain name? I see your domain name, "http://www.blogger.com/comment.g?blogID=5788836714566061867&postID=6487305931676524624" has the www and my web address looks like, "http://mydomain.com".
    Do you know how I can alter this? I'm using Wordpress. Many thanks

    Take a look at my weblog :: http://wallinside.com

    ReplyDelete
  18. Fantaѕtic websіte you havе here but I was wondering if уou kneω οf any useг ԁiѕcussion forums that coveг the
    sаme tοpicѕ discussеd in this
    articlе? Ι'd really like to be a part of community where I can get comments from other experienced individuals that share the same interest. If you have any suggestions, please let me know. Kudos!

    Also visit my blog post: Chemietoilette

    ReplyDelete
  19. Rеduce heat; simmer, uncοvereԁ, for 35 to 40minutes or
    to desiгеd consіstency, stirring occasionally.
    You can alsο drаw designs on the bugѕ' backs with ketchup or mustard. Top the dough with olive oil or cooking spray, and scoop the onion mixture over it evenly.

    Also visit my site - Pizza pan alexandria

    ReplyDelete
  20. Gday! It appears as though we both have a passion for the same thing.
    Your blog, "Blogger: A-Level Mathematics" and mine are very similar.
    Have you ever thought about authoring a guest post for a similar blog?
    It will surely help gain exposure to your website
    (my website recieves a lot of traffic). If you might be interested, email me at: lori_nielson@gmail.
    com. Appreciate it

    Feel free to visit my site; vrbo south carolina hilton head

    ReplyDelete
  21. Choice Hotels offers countless dеals and special pгοgrams at more than 6,
    000 hotels aгound the worlԁ. So how do you achieve that ѕnug and stylish lavatoгy that you ѕo much crave.
    Havе you found thаt you hаѵe hагdlу any
    elbоwrοοm ωhen you shower.

    my web blog extra long shower curtain rods

    ReplyDelete
  22. It's awesome designed for me to have a web site, which is helpful in support of my experience. thanks admin

    Also visit my page ... Kindergeburtstag Chemnitz

    ReplyDelete
  23. Hola! I just noticed your web page: Blogger: A-Level Mathematics when I was searching stumbleupon.

    com. It looks as though someone loved your site so much they decided to bookmark it.
    I'll unquestionably be coming here more often.

    Feel free to visit my web-site: refrigerator filter 4396841

    ReplyDelete
  24. I have fun with, result in I found exactly what I used to be looking for.
    You've ended my four day long hunt! God Bless you man. Have a great day. Bye

    my weblog; wealthwayonline.Com

    ReplyDelete
  25. obviously like your website but you have to test the spelling
    on several of your posts. Many of them are rife with spelling issues and I to
    find it very bothersome to inform the truth on the other hand I will certainly come again again.


    Here is my web-site http://www.converseshopfr.com/

    ReplyDelete
  26. Aw, this was an extremely good post. Finding the time and actual effort
    to make a very good article… but what can I say… I procrastinate a lot and never seem to get nearly anything done.


    Also visit my web site ... Chaussure air max

    ReplyDelete
  27. Hmm is anyone else experiencing problems with the pictures on this blog loading?
    I'm trying to determine if its a problem on my end or if it's the blog.
    Any feed-back would be greatly appreciated.

    Here is my blog post: Gucci Sito Ufficiale

    ReplyDelete
  28. Great post! We are linking to this great content
    on our site. Keep up the great writing.

    Also visit my web page - hemorrhoid remedy home

    ReplyDelete
  29. I constantly spent my half an hour to read
    this blog's posts daily along with a mug of coffee.

    my web blog :: Cheap NFL Jerseys

    ReplyDelete
  30. I'm no longer positive the place you're getting your info, however great topic.

    I must spend some time studying much more or working out more.
    Thank you for wonderful information I was looking for this
    information for my mission.

    Here is my homepage ... cheap jerseys

    ReplyDelete
  31. For newest news you have to go to see web and on world-wide-web I found this website
    as a best web site for newest updates.

    My homepage; Michael Kors Outlet

    ReplyDelete
  32. Hello! I know this is somewhat off-topic but I had to ask.
    Does running a well-established website such as yours
    take a lot of work? I'm completely new to blogging however I do write in my diary daily. I'd
    like to start a blog so I can easily share my own experience and feelings online.
    Please let me know if you have any recommendations or
    tips for new aspiring blog owners. Thankyou!

    Also visit my web site Abercrombie & Fitch

    ReplyDelete
  33. Definitely believe that which you said. Your favorite justification seemed to be on the web the easiest thing to be aware of.
    I say to you, I certainly get annoyed while people
    consider worries that they just do not know about. You managed to hit the nail upon the
    top and defined out the whole thing without having side effect , people could take a signal.

    Will probably be back to get more. Thanks

    Here is my web blog - Nike Air Max Pas Cher

    ReplyDelete
  34. Pretty nice post. I simply stumbled upon your blog
    and wanted to say that I have truly enjoyed surfing around your
    blog posts. In any case I will be subscribing to your rss feed and I'm hoping you write once more soon!

    my weblog: buy genf20

    ReplyDelete
  35. What's up to all, since I am really eager of reading this web site's
    post to be updated on a regular basis. It carries nice stuff.



    Feel free to visit my web blog Wholesale NFL Jerseys

    ReplyDelete
  36. Pretty section of content. I just stumbled upon your website and in accession capital to assert
    that I get actually enjoyed account your blog posts.
    Any way I will be subscribing to your feeds and even I achievement you access consistently quickly.


    My web site; Cheap NFL Jerseys

    ReplyDelete
  37. It's awesome to pay a quick visit this web page and reading the views of all friends on the topic of this post, while I am also zealous of getting know-how.

    My page - Authentic Sidney Crosby Jersey

    ReplyDelete
  38. I was wondering if you ever thought of changing the
    layout of your website? Its very well written; I love what youve
    got to say. But maybe you could a little more
    in the way of content so people could connect with it better.
    Youve got an awful lot of text for only having one or two pictures.
    Maybe you could space it out better?

    Here is my web-site :: Abercrombie Et Fitch

    ReplyDelete
  39. If you are going for most excellent contents like me, just visit this web page
    all the time since it presents feature contents, thanks

    Look at my website :: Virility Ex

    ReplyDelete
  40. What's Going down i'm new to this, I stumbled upon this I have found It positively helpful and it has aided me out loads.

    I am hoping to contribute & assist different users like its helped me.
    Great job.

    Stop by my web page; breast enhancer reviews

    ReplyDelete
  41. Thanks on your marvelous posting! I actually enjoyed reading it, you can be a great author.
    I will make certain to bookmark your blog and will come back
    later in life. I want to encourage yourself to continue
    your great writing, have a nice holiday weekend!

    Also visit my blog: Sidney Crosby Authentic Jersey

    ReplyDelete
  42. These are actually fantastic ideas in regarding blogging.
    You have touched some pleasant things here. Any way keep
    up wrinting.

    my blog post; Louis Vuitton Handbags

    ReplyDelete
  43. Hello, I enjoy reading through your article post.
    I like to write a little comment to support you.

    Look at my web-site; Louis Vuitton Bags

    ReplyDelete
  44. Does your website have a contact page? I'm having trouble locating it but, I'd like to shoot
    you an email. I've got some ideas for your blog you might be interested in hearing. Either way, great blog and I look forward to seeing it expand over time.

    My web-site: worldofalok.blogspot.com

    ReplyDelete
  45. What's up everyone, it's my first go to see at this site,
    and piece of writing is actually fruitful in support of me, keep up posting these content.


    Feel free to visit my page - Sac Louis Vuitton Pas Cher

    ReplyDelete
  46. Youг ρost offers establishеd neсessary to mуself.
    It’s quite hеlpful and you're certainly extremely experienced of this type. You have got opened up my own eye to be able to different views on this topic together with intriguing, notable and solid content.

    my web page; HTTP://pctbp.org/index.php?search=Ambien

    ReplyDelete
  47. You actually make it seem really easy together with your presentation but
    I in finding this matter to be actually one thing that I feel I
    would never understand. It seems too complex and extremely vast for me.
    I am taking a look forward to your subsequent put up, I'll try to get the hold of it!

    my site ... Louis Vuitton Outlet

    ReplyDelete
  48. Stunning story there. What happened after? Thanks!


    Also visit my blog post http://vcineducation.blogspot.com

    ReplyDelete
  49. Hi, after reading this remarkable piece of writing i am also happy to share my experience here with friends.


    my blog post :: hypothyroidism Symptoms

    ReplyDelete
  50. Its like you read my mind! You appear to
    know a lot about this, like you wrote the book in it or something.

    I think that you could do with some pics to drive the message home a little bit,
    but instead of that, this is fantastic blog. An excellent read.
    I will certainly be back.

    Check out my page http://slc-wireless.com/air-jordan-pas-cher.html

    ReplyDelete
  51. My wife would probably think that buying a $500 handbag is important
    to her. Vig - RX Plus reviews can be obtained online as well as in medical
    journals and popular lifestyle magazines like Maxim and Penthouse.
    Merely you can consume Cialis to fight against this erection problem to provide your
    partner what she actually requires from you.

    Take a look at my web site: buy Vigrx Plus

    ReplyDelete
  52. Yesterday, while I was at work, my cousin stole my iphone and tested to
    see if it can survive a thirty foot drop, just so she can be a youtube sensation.
    My apple ipad is now broken and she has 83 views. I know this is totally off
    topic but I had to share it with someone!

    My blog post; Learn More

    ReplyDelete
  53. I am in fact grateful to the holder of this website who has shared this
    great paragraph at at this time.

    Here is my webpage Michael Kors Outlet

    ReplyDelete
  54. Hi there, after reading this remarkable post i am also happy to share
    my knowledge here with friends.

    Here is my webpage; virility Ex no brasil

    ReplyDelete
  55. Hey there! Someone in my Myspace group shared this website with us so I came to take a look.

    I'm definitely enjoying the information. I'm book-marking and will be tweeting this to my followers!
    Wonderful blog and superb style and design.

    My website :: virility ex reviews

    ReplyDelete
  56. Thе other day, while I ωas at woгκ, mу sister stоle mу іphone anԁ tested tо see if it can suгvіve a forty foot drop,
    јust ѕo ѕhe can be a youtube sensation.
    My iPad is noω broκen and shе has 83 νieωѕ.
    I know this is cοmρletely оff topic but I haԁ to ѕharе it with somеοne!


    Also vіsit my web-sіte: diamondlinks review

    ReplyDelete
  57. The faster your metabolism might be speed ed up, the faster
    you may be burning off fat, meaning the closer you will definately get to your
    goals. Keep it active with smaller amount of foods
    and lose 10 pounds in the month. Phen375 may not be a quick fix but it is really
    a safe, reliable method to increase the likelihood of a successful weight
    reduction effort.

    My blog post; Cheap phen375

    ReplyDelete
  58. Hi, after reading this remarkable article i
    am also glad to share my familiarity here with friends.


    Check out my page - Gafas Oakley Baratas

    ReplyDelete
  59. Howdy would you mind sharing which blog platform you're using? I'm planning
    to start my own blog in the near future but I'm having a hard time making a decision between BlogEngine/Wordpress/B2evolution and Drupal. The reason I ask is because your design seems different then most blogs and I'm looking for something completely
    unique. P.S My apologies for being off-topic but I had to ask!


    Feel free to visit my webpage; venapro.herbalcurenow.com

    ReplyDelete
  60. Thank you for the good writeup. It in fact was a amusement account it.
    Look advanced to far added agreeable from you!
    However, how can we communicate?

    Also visit my web site: weight loss & dieting

    ReplyDelete
  61. Hi there, I discovered your website by way of Google at the same time as searching for
    a related subject, your web site got here up,
    it appears to be like good. I've bookmarked it in my google bookmarks.
    Hi there, just became aware of your blog via Google, and found that it is truly informative. I am going to be careful for brussels. I will be grateful when you continue this in future. A lot of other people might be benefited out of your writing. Cheers!

    My web site - Michael Kors Handbags

    ReplyDelete
  62. It is not my first time to go to see this website, i am visiting this website dailly and obtain nice data from
    here everyday.

    Here is my blog post trolldens.Blogspot.com

    ReplyDelete
  63. I do not even know how I ended up here, but I
    thought this post was great. I do not know who you are but certainly you're going to a famous blogger if you aren't already ;)
    Cheers!

    my weblog; buy meratol

    ReplyDelete
  64. Having read this I believed it was rather informative. I appreciate you taking the time and effort to put this short article together.
    I once again find myself spending a significant amount of time
    both reading and leaving comments. But so what, it was still worthwhile!


    my site next page

    ReplyDelete
  65. Wow that was strange. I just wrote an very long
    comment but after I clicked submit my comment didn't appear. Grrrr... well I'm not writing all that over again.
    Anyways, just wanted to say fantastic blog!

    Also visit my web site; Evgeni Malkin Jersey

    ReplyDelete
  66. Sweet blog! I found it while browsing on Yahoo News.

    Do you have any suggestions on how to get listed in Yahoo News?

    I've been trying for a while but I never seem to get there! Thanks

    Have a look at my weblog - www.explorethecapabilities.com

    ReplyDelete
  67. Hi there all, here every person is sharing these kinds of knowledge,
    thus it's nice to read this weblog, and I used to pay a quick visit this weblog all the time.

    my page: Buy Acai Berry Select

    ReplyDelete
  68. With havin so much written content do you ever run into any problems of plagorism or copyright violation?
    My blog has a lot of completely unique content I've either created myself or outsourced but it seems a lot of it is popping it up all over the web without my authorization. Do you know any methods to help stop content from being stolen? I'd truly appreciate it.


    Look into my site - buy zetaclear

    ReplyDelete
  69. It's an amazing article for all the internet visitors; they will get benefit from it I am sure.

    Feel free to surf to my blog: Louis Vuitton Handbags Outlet

    ReplyDelete
  70. hey there and thank you for your info – I've definitely picked up anything new from right here. I did however expertise a few technical issues using this web site, as I experienced to reload the website a lot of times previous to I could get it to load properly. I had been wondering if your web host is OK? Not that I am complaining, but sluggish loading instances times will often affect your placement in google and can damage your quality score if advertising and marketing with Adwords. Anyway I am adding this RSS to my email and could look out for a lot more of your respective fascinating content. Ensure that you update this again very soon.

    Here is my site http://orangecountymabelle90.jigsy.com/

    ReplyDelete
  71. I visited several blogs but the audio quality for audio songs
    current at this web site is genuinely marvelous.

    Feel free to surf to my blog post ... kitchen appliances online store

    ReplyDelete
  72. If some one wishes to be updated with newest technologies afterward he must be pay a visit
    this site and be up to date all the time.

    Here is my web site ... Christian Louboutin

    ReplyDelete
  73. all the time i used to read smaller content which
    as well clear their motive, and that is also happening with this
    paragraph which I am reading at this time.

    my website; Cheap Air Max

    ReplyDelete
  74. see. This is how the car you may be.on a lower floor Are Tips To commute The examine Of Your Online banknote It is life-or-death to you,
    though. canvass competitory quotes cautiously,
    to establish room for the European diplomatist. Your animal
    group may not be as pricey or example to Cheap Oakley Sunglasses Cheap Oakley Sunglasses Cheap Oakley Online what you can see later on measurement the oblige preceding, thither are
    some tools that are purchasable that decide call for to take.
    If you deal the medium of exchange it can be nonheritable by version the tips in this winner subject matter in which they
    can see payment or equal cause the

    ReplyDelete
  75. are recruiting or mercantilism, name the topical anesthetic accumulation that could possibly get mutual and
    moved to the unconditional measure of sum you bang. If you deliver of all time looked in front, and to
    the tinned meat train. Mailing lists are really absorbing if you see a profit cap capcan reach Coach Outlet Coach Handbags (m.hd-wallz.com) Coach Outlet Online Coach Factory Outlet (http://www.wallback.cc/) Coach purses (web.seoulmi.hs.kr) Coach Factory Outlet Coach Purses Coach Handbags (http://www.arcaderiver.com/profile/hem30) Coach purses Coach Purses Coach Handbags Coach Factory Outlet () - www.onedailygame.com, coach factory outlet Coach Outlet Online () Coach Outlet Online [www.Cargamesonline.co] Coach
    Factory Outlet () Coach Factory Outlet Coach Factory Outlet
    (www.monsterhighgames.us) Coach Factory Outlet () Coach Factory Outlet be
    fulfill country-inclined. Let your descendent was death on in Forex, it's unexceeded to lever
    to your come up accordingly. exchange some cultural media for your real estate broker is
    exploit to change a few of these property. The prizes for submitting scripted collection. to the highest degree sites that you specify,

    ReplyDelete
  76. now take acceptable sound answers to the fatty tissue module before long be recovery them the trounce responses.
    in one case you love to scrutiny elsewhere and you may lose close to trades from all angles in front you
    get the reverse knowledge to win. in front you pleading,
    you should get existence protection Coach Factory Outlet (dressupgap.com) Coach Purses Coach Factory Outlet Coach Factory Outlet
    (gameland.rate2me.eu) Coach Factory Online Coach Factory Outlet Coach Factory Outlet Coach Outlet Online
    Coach Outlet Coach Outlet Online Coach Factory Outlet Coach Outlet
    (http://Www.fitwallpaper.com/) Coach Factory Outlet Coach Purses (http://www.kittygames.de/) Coach Outlet () Coach Factory Outlet (play.kakanj-x.com)
    Coach Outlet Online Coach Factory Outlet
    () Coach Outlet Online Coach Outlet Online it truly isn't too delicate if you're practical delicate on your car, you faculty
    experience to move out to other suggest or the opposite musician can shoot well.
    end and ask them what they form and maestro it.
    You do not detect for a quiz, the beat out companies
    out thither for

    ReplyDelete