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Graph the following function using transformations. Find the vertical and horizontal...

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libbysimone | Salutatorian

Posted February 8, 2012 at 6:13 AM via web

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Graph the following function using transformations. Find the vertical and horizontal asymptotes. State the domain and range. Submit your graph f(x)=1/(x+1)3-3

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nathanshields | High School Teacher | (Level 1) Associate Educator

Posted February 8, 2012 at 7:18 AM (Answer #1)

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`f(x)=1/(x+1)^3-3`

First think about `1/x` .  It looks like this:

Now think about `1/x^2` .  Since `x^2` is always positive, so is the function:

Now what about `1/x^3` ?  Since `x^3` is negative when x is negative, the graph looks more like the top graph, 1/x.

Now, your function is just like `1/x^3` except the x has been adjusted with +1 and a -3 was thrown on the end.  So the graph is going to be translated 1 to the left and 3 down.

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