Answer: y > -1.5 which is the same as y > -3/2
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Step-by-step explanation:
As x goes off to negative infinity, the term 3^x gets closer to 0.
So the expression 0.5*(3^x - 3) approaches 0.5*(0-3) = 0.5*(-3) = -1.5 = -3/2
The y value will never actually get to -1.5 because 3^x never actually reaches 0. It only gets closer and closer.
So the range is the set of possible y outputs such that y > -1.5 or y > -3/2
This means the horizontal asymptote is y = -3/2 or y = -1.5 which is the horizontal "electric fence" of sorts that the function curve gets closer to, but never touches.