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Thread: HELP Isotope questions

  1. #1
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    HELP Isotope questions

    What are the asymptotes of the graph of y= 3 + 5 ?
    2x-6


    What are the asymptotes of the graph of y = 2 -7 ?
    x+18

    The variable z varies directly with y and inversely with x. When x-4 and y = 28, z = 56. Which equation relates to x, y, and z?

    z = 8y
    X
    z= xy
    56

    z= 8xy
    z= 56xy

    Is there anyone that can help me??? PLEASE a mom that has long since forgotten this stuff trying to help daughter!!!
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  2. #2
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    Quote Originally Posted by chessmaster View Post
    What are the asymptotes of the graph of y= 3 + 5 ?
    2x-6



    What are the asymptotes of the graph of y = 2 -7 ?
    x+18

    The variable z varies directly with y and inversely with x. When x-4 and y = 28, z = 56. Which equation relates to x, y, and z?

    z = 8y
    X
    z= xy
    56

    z= 8xy
    z= 56xy

    Is there anyone that can help me??? PLEASE a mom that has long since forgotten this stuff trying to help daughter!!!
    If I'm reading what you have written correctly, you would like to find the asymptotes of $\displaystyle y = \frac{3}{2x-6} + 5$ and $\displaystyle y = \frac{2}{x + 18} - 7$. An asymptote is simply a function that the graph approaches for increasing or decreasing values of x. And in these cases, the important factor is that x is in the denominator. When you have x in the denominator, the constant part of the denominator becomes less important for increasing values of x. So for the first question, the asymptote is $\displaystyle y = \frac{3}{2x} + 5$ and for the second question, the asymptote is $\displaystyle y = \frac{2}{x} - 7$. The correct answer to your proportionality question is $\displaystyle z = \frac{8y}{x}$. This is because when two variables a and b are directly proportional, they are related by $\displaystyle a = kb$ for some constant k, and when a and b are inversely proportional, they are related by $\displaystyle a = \frac{k}{b}$ or $\displaystyle ab = k$ for some constant k.
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  3. #3
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    Quote Originally Posted by icemanfan View Post
    If I'm reading what you have written correctly, you would like to find the asymptotes of $\displaystyle y = \frac{3}{2x-6} + 5$ and $\displaystyle y = \frac{2}{x + 18} - 7$. An asymptote is simply a function that the graph approaches for increasing or decreasing values of x.

    Mr F says: You are referring to a particular type of asymptote known as an oblique asymptote. Horizontal asymptotes are a special case of such asymptotes.

    There is another type of asymptote known as a vertical asymptote. These asymptotes are vertical lines passing through values of x that make the function undefined.

    And in these cases, the important factor is that x is in the denominator. When you have x in the denominator, the constant part of the denominator becomes less important for increasing values of x. So for the first question, the asymptote is $\displaystyle y = \frac{3}{2x} + 5$ and for the second question, the asymptote is $\displaystyle y = \frac{2}{x} - 7$.

    Mr F says: NO! This is wrong.

    [snip]
    $\displaystyle y = \frac{3}{2x-6} + 5$:

    Vertical asymptote found by solving 2x - 6 = 0: x = 3.

    Horizontal asymptote found by considering the limits x --> oo and x --> -oo: $\displaystyle y \rightarrow 0 + 5 = 5$.

    --------------------------------------------------------------------------

    $\displaystyle y = \frac{2}{x + 18} - 7$.

    Vertical asymptote found by solving x + 18 = 0: x = -18.

    Horizontal asymptote found by considering the limits x --> oo and x --> -oo: $\displaystyle y \rightarrow 0 - 7 = -7$.
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  4. #4
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    Quote Originally Posted by chessmaster View Post
    [snip]
    The variable z varies directly with y and inversely with x. When x-4 and y = 28, z = 56. Which equation relates to x, y, and z?

    z = 8y
    X
    z= xy
    56

    z= 8xy
    z= 56xy

    Is there anyone that can help me??? PLEASE a mom that has long since forgotten this stuff trying to help daughter!!!
    $\displaystyle z = \frac{k y}{x}$.

    Substitute the given data: $\displaystyle 56 = \frac{28 k}{4} = 7k \Rightarrow k = 8$.

    Therefore $\displaystyle z = \frac{8 y}{x}$.
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