Answer: Choice A
-infinity < y < 2
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Explanation:
The range is the set of possible y outputs of a function.
What's the smallest y can get? The answer here is there is no smallest y value as the graph heads off downward forever. So we say negative infinity is the lower bound. So we can say -infinity < y
What's the largest y can get? That would be y = 2. It can't actually get to y = 2 as this is a horizontal asymptote. The graph approaches this horizontal line getting closer and closer, but never actually arriving there. So we can say y < 2
Combine -infinity < y and y < 2 to get -infinity < y < 2
It's much simpler to write y < 2 without the "-infinity < y" portion, but the more expanded out way helps us convert to interval notation which would be (-infinity, 2). The curved parenthesis tell the reader "do not include the endpoint as part of the set". Infinity is not a number, and you can't reach infinity, so there is no way to include it as a set of real numbers.
