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Math Help - Functions and Transformations Project.

  1. #1
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    Functions and Transformations Project.

    Hi guys! i'm new here at the forum. just got a math project on functions and transformations, but had some problems with the last part. so i need some urgent help as i have 2 more days untill the project is due. so here we go:

    we were given a basic function f(x)=x^2. we were told to graph it and compare it to the graphs of various other functions. we were also asked to deduce the graphs and produce a table of results. so here is what i came up with:

    Type of Transformation
    Effect on Graph of f(x)
    1
    f(x) +c , c > o
    upward shift by c


    2
    f(x) +c , c < o
    downward shift by c


    3
    f(x + c), c >0
    horizontal shift to left by c


    4
    f(x + c), c < 0
    horizontal shift to right by c


    5
    -f(x)
    reflection in x axis


    6
    f(-x)
    reflection in y axis


    7
    α f(x), α > 1
    vertical stretch by a


    8
    α f(x), 0 < α < 1
    vertical compression by a


    9
    fx), α > 1
    horizontal compression by a


    10
    fx), 0 < α < 1
    horizontal stretch by a




    now ill just post the final part from the project:

    Part VIII


    In this final part of the Project you and your group members are to use the knowledge gained from Parts I-VII to apply the rules of functional transformations to a function γ(x) where the formula is not known, but the graph ofγ(x) is known. On the last page of the lab is the graph of a function γ(x) for which the algebraic formula is unknown. Using the information gained in this lab, draw the graph of a new function β(x) defined according to β(x) = 1/2(1 - γ(-2x)) + 1.
    Be sure to fully explain your reasoning in deducing the graph of β(x) in your final lab report.




    now from my understanding, i have to transform the graph given above using the formula for b(x) above. but the formula is just so complicated that i cant understand what i need to do. any help will be greatly appreciated.
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  2. #2
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    Quote Originally Posted by satish555 View Post
    Hi guys! i'm new here at the forum. just got a math project on functions and transformations, but had some problems with the last part. so i need some urgent help as i have 2 more days untill the project is due. so here we go:

    we were given a basic function f(x)=x^2. we were told to graph it and compare it to the graphs of various other functions. we were also asked to deduce the graphs and produce a table of results. so here is what i came up with:

    Type of Transformation
    Effect on Graph of f(x)
    1
    f(x) +c , c > o
    upward shift by c


    2
    f(x) +c , c < o
    downward shift by c


    3
    f(x + c), c >0
    horizontal shift to left by c


    4
    f(x + c), c < 0
    horizontal shift to right by c


    5
    -f(x)
    reflection in x axis


    6
    f(-x)
    reflection in y axis


    7
    α f(x), α > 1
    vertical stretch by a


    8
    α f(x), 0 < α < 1
    vertical compression by a


    9
    fx), α > 1
    horizontal compression by a


    10
    fx), 0 < α < 1
    horizontal stretch by a




    now ill just post the final part from the project:

    Part VIII


    In this final part of the Project you and your group members are to use the knowledge gained from Parts I-VII to apply the rules of functional transformations to a function γ(x) where the formula is not known, but the graph ofγ(x) is known. On the last page of the lab is the graph of a function γ(x) for which the algebraic formula is unknown. Using the information gained in this lab, draw the graph of a new function β(x) defined according to β(x) = 1/2(1 - γ(-2x)) + 1.
    Be sure to fully explain your reasoning in deducing the graph of β(x) in your final lab report.




    now from my understanding, i have to transform the graph given above using the formula for b(x) above. but the formula is just so complicated that i cant understand what i need to do. any help will be greatly appreciated.


    Draw a diagram for each of these steps.

    \gamma(-x) is your reflection in the y-axis.

    \gamma(-2x) is your horizontal compression.

    -\gamma(-2x) is a reflection in the x-axis.

    1 - \gamma(-2x) is a vertical shift upwards by 1 unit.

    \frac{1}{2}[1 - \gamma(-2x)] is vertical compression.

    \frac{1}{2}[1 - \gamma(-2x)] + 1 is a vertical shift upwards by 1 unit.
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  3. #3
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    Quote Originally Posted by satish555 View Post
    Hi guys! i'm new here at the forum. just got a math project on functions and transformations, but had some problems with the last part. so i need some urgent help as i have 2 more days untill the project is due. so here we go:

    we were given a basic function f(x)=x^2. we were told to graph it and compare it to the graphs of various other functions. we were also asked to deduce the graphs and produce a table of results. so here is what i came up with:



    Type of Transformation



    Effect on Graph of f(x)

    1

    f(x) +c , c > o

    upward shift by c


    2

    f(x) +c , c < o

    downward shift by c


    3

    f(x + c), c >0

    horizontal shift to left by c


    4

    f(x + c), c < 0

    horizontal shift to right by c


    5

    -f(x)

    reflection in x axis


    6

    f(-x)

    reflection in y axis


    7

    α f(x), α > 1

    vertical stretch by a


    8

    α f(x), 0 < α < 1

    vertical compression by a


    9

    fx), α > 1

    horizontal compression by a


    10

    fx), 0 < α < 1

    horizontal stretch by a




    now ill just post the final part from the project:

    Part VIII


    In this final part of the Project you and your group members are to use the knowledge gained from Parts I-VII to apply the rules of functional transformations to a function γ(x) where the formula is not known, but the graph ofγ(x) is known. On the last page of the lab is the graph of a function γ(x) for which the algebraic formula is unknown. Using the information gained in this lab, draw the graph of a new function β(x) defined according to β(x) = 1/2(1 - γ(-2x)) + 1.
    Be sure to fully explain your reasoning in deducing the graph of β(x) in your final lab report.




    now from my understanding, i have to transform the graph given above using the formula for b(x) above. but the formula is just so complicated that i cant understand what i need to do. any help will be greatly appreciated.

    Try breaking it up into "pieces" (that way you may better explain what is going on..using previous knowledge).
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  4. #4
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    Nov 2008
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    thanx a lot guys! really helpful.
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