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Thread: Unable to understand this question about graph transformation

  1. #1
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    Unable to understand this question about graph transformation

    The question is probably very simple but I just can't seem to understand what it wants.
    Unable to understand this question about graph transformation-math.png
    I've drawn out both of the graphs alongside their asymptotes is that all it wants? Am I overthinking this question?
    It says to transform but I don't know how to transform between these two/ which one I transform from.
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  2. #2
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    Re: Unable to understand this question about graph transformation

    Well the problem asks you to use the graph of $\displaystyle y= \frac{1}{x}$ to graph this new function. I presume that you know that the graph of $\displaystyle y= \frac{1}{x+ 1}$ is just the graph of $\displaystyle y= \frac{1}{x}$ shifted to the left one unit. So how does multiplying that by x change the graph?
    Last edited by topsquark; Aug 9th 2018 at 12:28 PM.
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  3. #3
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    Re: Unable to understand this question about graph transformation

    I would use the fact that

    $$\dfrac{x}{x+1} = \dfrac{(x+1)-1}{x+1} = \dfrac{x+1}{x+1} - \dfrac{1}{x+1} = 1 - \dfrac{1}{x+1}$$

    along with the hint HallsofIvy gave you.
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  4. #4
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    Re: Unable to understand this question about graph transformation

    So quickly drawing it out as 1/x and then 1/x+1 and finally x/x+1 I get the following -
    Unable to understand this question about graph transformation-1-x.pngUnable to understand this question about graph transformation-1-x-1.pngUnable to understand this question about graph transformation-x-x-1.png
    I can say that it moves to the left once and then it gets reflected and moves up by 1 when numerator 1 is replaced with x?
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  5. #5
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    Re: Unable to understand this question about graph transformation

    Correct.
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