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Math Help - Graph of a function

  1. #1
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    Graph of a function

    1. Write down the range of values of x for which the graph of y = f(x) has a negative gradient.
    I don't even know where to start with the first step.

    2. The equation f(x) + x 1 = 0 can be solved by drawing a line on the grid.

    (i) Write down the equation of this line. [1]

    (ii) How many solutions are there for f(x) + x 1 = 0?
    They're talking about a tangent line, yes? So where do I draw it?

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  2. #2
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    negative gradient  x \in (0,6)

    Can you see why?
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  3. #3
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    I think its because the gradient between y=0 and y=6 is sloping downwards to the right?
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  4. #4
    Junior Member mathbuoy's Avatar
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    Q1

    x=0 to x=6

    Q2

    y=-x+1

    get some points for the line,
    x=0, y=1
    x=1, y=0

    plot the line then count number of intersection points.
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  5. #5
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    Oh ok thanks I understand Q. 2, however I'm still stuck with Q. 1.
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  6. #6
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by yorkey View Post
    I think its because the gradient between y=0 and y=6 is sloping downwards to the right?
    What is the definition of a negative gradient? Surely your text tells you that much?

    -Dan
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  7. #7
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    Quote Originally Posted by topsquark View Post
    What is the definition of a negative gradient? Surely your text tells you that much?

    -Dan
    A negative gradient slopes down and to the right. Actually, I think I get it now.

    "...graph of y = f(x) has a negative gradient. " There's only one negative slope, so the answer is the start and end values of the slope on the x-axis. The slope starts at (0,3) and ends at (6,-9) so the answer is 0 and 6. Is my reasoning right?
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  8. #8
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by yorkey View Post
    A negative gradient slopes down and to the right. Actually, I think I get it now.

    "...graph of y = f(x) has a negative gradient. " There's only one negative slope, so the answer is the start and end values of the slope on the x-axis. The slope starts at (0,3) and ends at (6,-9) so the answer is 0 and 6. Is my reasoning right?
    Yup!

    -Dan
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  9. #9
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    Awesome, you guys rock.
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