Finding Limits from a graph

Question

This question shows a graph y=b(x) an exponential graph that is does not have an reflection over x or y but has the point (3,0) and Horizontal Asymptote of -2. What is the limits as it x goes to infinite and negative infinite? And how could I express y=|b(x)| as a piecewise function? How do I write an equation for h(x) if h(x) = b(x) but x cannot equal 3?

(I can’t show the graph but I explained it the best I could)

Answer 1

If the exponential function is increasing, then the limit of the function as x→∞ is ∞, and as x→-∞ the function's limit is -2.

If the exponential function is decreasing, then the limit of the function as x→-∞ is ∞, and as x→∞ the function's limit is -2.

Note: the fact that (3,0) is a point on the function only tells me that the curve is above y = -2. It does not tell me whether the curve is increasing or decreasing. A second point would tell me that, or a look at the graph.

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| -b(x) for x<0

y = | b(x) for x≥0

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h(x) = b(x) for x≠0