Find the horizontal asymptote of the function .
Function by following steps:
step0: Find the horizontal asymptotes:
step1: Evaluate the limits and
step2: Calculate:
step3: The finite values are horizontal asymptotes:
The horizontal asymptote of the function is .
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To find the domain of the function , we need to determine where the function is defined. It is undefined at since that makes the denominator zero. Therefore, the domain can be expressed as all real numbers except : .
As for the range, the horizontal asymptote indicates that as approaches positive or negative infinity, approaches 2, but never actually reaches it. Since there are no restrictions on except this asymptote, the range is .