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Thread: 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 $\displaystyle f(x)$ crosses the $\displaystyle x$-axis: $\displaystyle x = 0$ and $\displaystyle x = 4$. These two points divide the $\displaystyle x$-axis into 3 intervals:

    • $\displaystyle x \le 0$


    • $\displaystyle 0 \le x \le 4$


    • $\displaystyle 4 \le x$

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

    So, which one(s) is it?

    Grandad
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  5. #5
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    I think the answer is $\displaystyle
    0 \le x \le 4
    $
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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 $\displaystyle f(x) \le 0$.

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

    Grandad
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  7. #7
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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 $\displaystyle x$ 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, $\displaystyle h$ is the vertical distance
    between the y-coodinate and a horizontal asymptote of 2.

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

    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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