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Math Help - graphing functions

  1. #1
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    graphing functions

    For this question I am supposed to graph the function and determine the interval(s) (if any) on the real axis for which f(x) is greater than or equal to 0. My question is this: f(x) = x^2 - 4x
    Can you help me with it?

    Thank you for your time,
    starrynight
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  2. #2
    MHF Contributor red_dog's Avatar
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    See where the graph is above the x-axis.
    Attached Thumbnails Attached Thumbnails graphing functions-graph.jpg  
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  3. #3
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    Quote Originally Posted by red_dog View Post
    See where the graph is above the x-axis.
    I get the graph but how do I find the intervals?
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  4. #4
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    Hello starrynight
    Quote Originally Posted by starrynight View Post
    I get the graph but how do I find the intervals?
    Look at where the graph of f(x) crosses the x-axis: x = 0 and x = 4. These two points divide the x-axis into 3 intervals:

    • x \le 0


    • 0 \le x \le 4


    • 4 \le x

    The question asks you for the interval(s) for which f(x) \ge 0. In other words, in which of the three intervals above is the graph of f(x) on or above the x-axis.

    So, which one(s) is it?

    Grandad
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  5. #5
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    I think the answer is <br />
0 \le x \le 4<br />
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  6. #6
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    No, this is the interval where the graph goes below the x-axis; in other words, where f(x) \le 0.

    So you want the two intervals x \le 0 and 4 \le x.

    Grandad
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  7. #7
    Math Engineering Student
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    Quote Originally Posted by starrynight View Post
    For this question I am supposed to graph the function and determine the interval(s) (if any) on the real axis for which f(x) is greater than or equal to 0. My question is this: f(x) = x^2 - 4x
    Can you help me with it?

    Thank you for your time,
    starrynight
    Following up on red_dog's graph, for each x you need to get a positive or null image, can you see what are those intervals then?
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  8. #8
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    graphing/writing functions

    I am having trouble with problem 74. I don't really know how to approach the problem. The directions say to write the height , h , as a function of x.

    I would highly appreciate it if someone could help me out.
    --Thanks
    Attached Thumbnails Attached Thumbnails graphing functions-xs01010.gif  
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  9. #9
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    h = 2 - x^(1/3) ?
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  10. #10
    Newbie Deco's Avatar
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    As far as I can see, h is the vertical distance
    between the y-coodinate and a horizontal asymptote of 2.

    So simply, h= |2-\sqrt[3]{x}|

    Strictly speaking, I don't think the absolute value is needed.
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  11. #11
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    So following up on songoku and Deco, is the correct form of writing the function with the square root or should i leave it as x^1/3?

    --Thanks again.
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  12. #12
    Newbie Deco's Avatar
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    It's a cube root, and they both represent the exact same thing.
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