# How do you find the range of a function algebraically #y=(x+5)/(x-2)#?

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To best way to find the range of a function is to find the domain of the inverse function. To find the inverse function of a function you have to substitue

So:

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There will be a break in the range at any horizontal asymptote.

Since the degree of the numerator and denominator are equal, take and divide the coefficients of the terms with the largest degree.

Both of these terms are

The range is

graph{((x+5)/(x-2)-y)(y-1)=0 [-28.45, 29.27, -12.3, 16.57]}

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