Question

given, what are the domain and range?

Answer 1

Factor the rational function,

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Notice that the denominator and numerator both have x-1. This means that we have a removable discontinuity there so set x-1=0.

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So our domain can be all reals except 1.

Range: First factor out the x-1. We will be left with

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Since 1 isn't in the domain, plug in 1 to find the what won't be in the range

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So 7 isn't in the range,

End Behavior:

Since the rational function numerator is a quadratic and the denominator is a linear function, the rational function will approach will not have a horizontal asymptotes.