Identify the asymptotes, domain, and range of the function.
𝑓(𝑥) = 3/ (𝑥 + 2) + 1
In this case, since there is no variable in the numerator there will be a horizontal asymptote at y=0, but in this case there is a transformation of +1. So the horizontal asymptote is as y=0+1=1. There is a vertical asymptote when the function is undefined. the function will be undefined when the denominator of the 3/(x+2) term is zero. this happens at x+2=0, or x=-2.
The domain of a function is the list of all possible inputs. we know the function is undefined at x=-2, so the domain is x not = -2.
The range is all possible outputs of the function. This function has a range of y not = 1.