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Let
Find the range of $$f(x) = \frac{3x - 7}{x + 1}.$$. Give your answer as an interval $$f$$.

I am having trouble with this problem. Can someone please help me. Thanks so much. Please explain how you got the answer because I want to know how to solve the problem.

ant101  Apr 2, 2017
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f(x)  = [ 3x - 7 ] / [ x + 1 ]

For rational functions like this that have the same power poynomials in the numerator and denominator.......we can find the horizontal asymptote by dividing the term with the greatest power in the numerator by the term with the greatest power in the denominator.....so

3x / [ (1)x ]  =  3

So.....we will have a horizontal asymptote at  y = 3

And as x approaches -1 from the left, y →  infinity

And as x approaches -1 from the right, y → -infinity

So....the range is  (-infinity, 3) U (3, + infinity )

Here's a graph showing this : https://www.desmos.com/calculator/dq3shmjv9x

CPhill  Apr 2, 2017

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