Question #104079
Obtain the largest possible domain, and corresponding range, of the function f, defined by f(x)=(x-2)/(3-x)
Expert's answer
f(x)=(x-2)/(3-x)=-1-(1/(x-3)).
The asymptotes of the graph are y = -1 and x = 3.
The domain of the function: x∈(-∞,3)∪(3,+∞).
The range of the function: y∈(-∞,-1) ∪(-1,+∞).
It increases when x∈(-∞,3) and increases when x∈(3,+∞).
