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    I have a couple of questions regarding graph transformations. first, say you were asked to stretch the graph of y=x^2+4x+2 in the x direction by scale factor 3, what would you do. the function would be y=f(3x) wouldnt it, but im unsure?

    secondly, how would you notate a transformation in terms of vectors? so if the graph of y=x^2 was moved 2 units left and one up, would the vector be -2 over 1 or 2 over 1?
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    (Original post by Bertybassett)
    I have a couple of questions regarding graph transformations. first, say you were asked to stretch the graph of y=x^2+4x+2 in the x direction by scale factor 3, what would you do. the function would be y=f(3x) wouldnt it, but im unsure?

    secondly, how would you notate a transformation in terms of vectors? so if the graph of y=x^2 was moved 2 units left and one up, would the vector be -2 over 1 or 2 over 1?
    1) Because it wants you to stretch on the x-axis by S.F. 3, the function would be y=f(x/3). If the transformation affects X, you need to do the opposite. If it was SF 2 it would be f(x/2). Likewise if it was SF of 2/3, the function would be f(3x/2).

    If the stretch was in the Y it would be 3f(x) etc.

    2) Using vector notation to describe a graph translation is always x over y. E.g if y=x^2 was moved 2 units left and one up, the vector would be -2 over 1.

    I hope I've answered your questions.
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    (Original post by _RobbieL_)
    1) Because it wants you to stretch on the x-axis by S.F. 3, the function would be y=f(x/3). If the transformation affects X, you need to do the opposite. If it was SF 2 it would be f(x/2). Likewise if it was SF of 2/3, the function would be f(3x/2).

    If the stretch was in the Y it would be 3f(x) etc.

    2) Using vector notation to describe a graph translation is always x over y. E.g if y=x^2 was moved 2 units left and one up, the vector would be -2 over 1.

    I hope I've answered your questions.
    thank you, for the first one how would you work out the actual equation of the line of the graph from that function e.g. assuming the graph is y=x^2=2x+1 and you need the equation of the line from the function f(3x) or say 4f(x)
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    (Original post by Bertybassett)
    thank you, for the first one how would you work out the actual equation of the line of the graph from that function e.g. assuming the graph is y=x^2=2x+1 and you need the equation of the line from the function f(3x) or say 4f(x)
    just replace each "x" with "x/3"
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    (Original post by _RobbieL_)
    If the transformation affects X, you need to do the opposite.
    (Original post by Bertybassett)
    ...
    A helpful tip would be 'not JUST for x'. If you have y=f(x) and the transformation takes place parallel y-axis, then it's much easier to remember transformations as "Just do the opposite to the said variable". So a translation by -5 in the y-direction would make y+5=f(x) or a stratch by s.f. 1/2 in the y-dir means 2y=f(x) which may seem a bit pointless on their own, but in orders of multiple transformations along y or x-axis, these would help think about the problems on much simpler ground.
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    (Original post by the bear)
    just replace each "x" with "x/3"
    Bear is right
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    (Original post by the bear)
    just replace each "x" with "x/3"
    is that if the function was f(x/3) ??
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    (Original post by Bertybassett)
    is that if the function was f(x/3) ??
    for where you wanted to stretch it in the x direction.
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    (Original post by _RobbieL_)
    Bear is right
    would that be if the function was f(x/3) then. also if the function was say 4f(x) would yu times the the whole equation by 4.
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    (Original post by Bertybassett)
    is that if the function was f(x/3) ??
    Yes. If it wants you to find a new equation under a certain stretch you just change every x for what is inside the f(?)
 
 
 
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