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Math Help - Absolute Value Question (Grade 11)

  1. #1
    s3a
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    Absolute Value Question (Grade 11)

    How do I find the rule?
    Attached Thumbnails Attached Thumbnails Absolute Value Question (Grade 11)-0010.jpg  
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  2. #2
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    level decreases at a constant rate ... H(n) is a linear function.

    take two values for (n, H(n)) ...

    (0, 86) (3, 68)

    determine the slope ...

    \frac{\Delta H}{\Delta n} = \frac{68 - 86}{3 - 0} = -6

    use the point-slope form for a linear equation ...

    H(n) - 86 = -6(n - 0)

    H(n) = 86 - 6n
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  3. #3
    s3a
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    I'm still a little confused from your explanation.
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  4. #4
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    Quote Originally Posted by s3a View Post
    I'm still a little confused from your explanation.
    What part is confusing you? Skeeter found the slope using two points and then, equation of line.
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  5. #5
    s3a
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    Is one of those points the vertex? Aren't those 3 points in a straight line; like I can't get the equations of two linear functions and find the vertex by finding their point of intersection if they're straight. Sorry if I've missed something, I'm a bit tired from studying all day.
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  6. #6
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    what makes you think this problem involves an absolute value function?
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  7. #7
    s3a
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    My solution guide says:

    f(x)=6|x-6|+50

    but doesn't show work. I too had a problem figuring what it was at first but what else could it be?
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  8. #8
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    the absolute value function accounts for the increase in the water level from the 6 month to the 12 month time period.

    the function I completed works for the first 6 months only.

    question should have stated that a bit more clearly.
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  9. #9
    s3a
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    Yes it really should have. You're the 3rd person it confused. Anyway, can you please show me how to do this in an absolute function way please so I can understand it because I am studying for an exam.
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  10. #10
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    are you familiar with graphical transformations of the parent function y = |x| ?
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  11. #11
    s3a
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    You mean by adding the a,b,h,k paramaters? Yes, I am familiar with that.
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  12. #12
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    having to find an absolute value function, I would sketch a graph with points at (0,86) (3,68) (6,50) (9,68) (12,86).

    connecting the points using lines, one can see the large "V" indicating a transformed version of y = |x|.

    slope is \pm 6 ...

    y = 6|x|

    horizontal shift to the right 6 units ...

    y = 6|x-6|

    vertical shift up 50 units ...

    y = 6|x-6| + 50

    but, again, the problem statement should have been more clear in relating what was required as a solution.
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