Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

Graph transformations - explanation

Announcements Posted on
Applying to Uni? Let Universities come to you. Click here to get your perfect place 20-10-2014
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    Hi i am uncertain about the following, well i have this question which says:

    The original graph is y = sqrt(x) and takes the following transformations y = sqrt(-x)

    Now I have to describe the transformation in words, and to me wouldn't it be a reflection about y-axis? because it is a vertical reflection about the vertical axis right? However my answers say it is a reflection about the the x-axis which i cant seem to understand. If it were the x-axis wouldnt it be a reflection about the x-axis?

    Please any help would be great!
    • 0 followers
    Offline

    ReputationRep:
    You are confusing y=sqrt(-x) with y=-sqrt(x). We know that the sqrt fn is always positive (assuming x is real), so a reflection about y=0 (x axis) is impossible as this would make sqrt(x) negative.

    Think about it this way:
    for which x is y=sqrt(x) undefined?
    for which x is y=sqrt (-x) undefined?
    what is the relationship between these two sets of numbers

    is there an x for which x=-x (and so sqrt(x)=sqrt(-x) - this point will have to be on the axis of reflection so that it is not moved).
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    ah ok thanks for that. So in terms of describing transformations for graphs how can i tell the difference like when it is a dilation parallel to y-axis or dilation parallel to x-axis, this really confuses me :/. for example y = x^2 --> y = 2x^2, is this a dilation parallel to the y-axis scale factor 2? (parallel to y-axis because it is vertical?)

    And also like y = x^2 --> y = (2x)^2 would that be dilation parallel to x-axis scale factor 1/2 because it is a horizontal dilation?

    Thanks
    • 0 followers
    Offline

    ReputationRep:
    In general, if the 'change is being made to x (ie, before the fn is performed on it (usually f(ax) or f(x-a) or f(ax+b) where a and b are constant (but not necessarily positive), then it will be in the x direction

    so a translation in the case of f(x-a) - translate the graph by a units (in the positive x direction). This will result in moving the graph to the left (in the negative x direction) if a is negative. Be careful about signs. if you have f(x+a) think of it as f(x-(-a)) or reverse positive and negative direction in the above.
    'stretch' in the case of f(ax) by a factor of 1/a (so for f(2x), its a stretch by factor 1/2 in x direction ONLY - so eg x^2 to (2x)^2 then the points (-2,4), (-1,1), (0,0) would go to (-1,4), (-1/2,1), (0,0) respectively). If a is negative, then you can think of it as a reflection in y axis (x direction) followed by 'stretch' of factor 1/mod(a) (this was the case in your ex. sqrt(x) -> sqrt(-x) reflection in y axis, followed by 'stretch of factor 1/1 = 1 (this does not change anything).

    If the change is being made AFTER the fn is performed so you have af(x)+b (where a and b are constants, not necessarily positive, one or both could be zero) then the change is in the y direction. Similar rules apply to the ones above, except that the factor for stretches is just a (not 1/a).

    And, this applies to transformations in both directions, always do stretches before translations (unless you have something like f(2(x+3)). But even then its probably easier/safer to just expand it out to f(2x+6) and then do f(x)->f(2x)->f(2x+6).

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: April 1, 2012
New on TSR

Personal statement help

Use our clever tool to create a PS you're proud of.

Article updates
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.