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Math Help - Graph this function

  1. #1
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    Question Graph this function

    Graph: f(x)=3(1-e^{-x}), for nonnegative values of x.

    Of course I could plug in numbers, but I think they want me to employ some properties of logarithms to make graphing easier.

    I see the vertical stretching of 3 and horizontal translation of -1. I believe the -x will flip it across the y-axis... Any Ideas?
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  2. #2
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    Quote Originally Posted by ChristopherDunn View Post
    Graph: f(x)=3(1-e^{-x}), for nonnegative values of x.

    Of course I could plug in numbers, but I think they want me to employ some properties of logarithms to make graphing easier.

    I see the vertical stretching of 3 and horizontal translation of -1. I believe the -x will flip it across the y-axis... Any Ideas?


    Let y=f(x). Logarithms won't help much because of the \ln(1-e^{-x}) term which wouldn't help much.


    IMO the best way to go about it is to find the points of intersection with the axes and any asymptotes after distributing the 3 and then draw a curve similar to -\frac{1}{x}

    Spoiler:
    For example we know that as x \rightarrow \infty then e^{-x} \rightarrow 0 so there will be an asymptote at y=3

    Similarly to find the point of intersection on the x axis solve f(0)

    f(0) = 3(1-1) = 0 hence (0,0) is a point.


    You can then transform the graph left by 1 unit.

    Note how the graph below is similar to y=1-\frac{1}{x} which is shown in green


    edit: on the graphs I have restricted the domain to x>0 as that is what your question states

    edit 2: I'm a fool, I misunderstood what you meant by the -x (I think)
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  3. #3
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    hhmmmm I think I got it a different way...

    let f(x)=e^x
    f(-x)=e^{-x}
    -f(-x)=-e^{-x}
    -f(-x)+1=-e^{-x}+1
    3(-f(-x)+1)=3(-e^{-x}+1)

    reducing to -3(f(-x)-1)


    so I can graph e^x, and then working from the inside out, flip it across the y axis (-x), translate vertically down one (-1), then flip over x-axis and stretch by 3 (-3). That all seems more complicated than picking points, though....

    I had had originally thought that they wanted me to use logs because that is what the chapter is about... but it is also about exponential functions.
    Attached Thumbnails Attached Thumbnails Graph this function-eq.jpg  
    Last edited by ChristopherDunn; May 23rd 2010 at 11:19 PM.
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