Answer to Question #104079 in Calculus for Sourav Mondal

Question

Obtain the largest possible domain, and corresponding range, of the function f, defined by f(x)=(x-2)/(3-x)

Answer 1

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,+∞).