Answer
The Domain is (-∞, ∞)
The Range is (-∞, 6)
The horizontal asymptote is at y = 6
See graph below.
Work Step by Step
Given $f(x) = 6 - 3^x$
The transformations are as follows
The red graph represents the graph of $3^x$
The blue graph represents the graph of $(-3)^x$, which is a reflection about the x-axis of the red graph
The green graph represents the graph of $f(x)$, which is a translation of 6 units up from the blue graph
The Domain is (-∞, ∞)
The Range is (-∞, 6)
The horizontal asymptote is at y = 6