An exponential function with a horizontal asymptote at y = -2 will be of the form:
f(x) = 2^(-x) - 2
Which of the following exponential functions has a horizontal asymptote at y = -2?
An exponential equation will have a horizontal asymptote when the exponent, x, has a negative sign. This will cause that as x tends to infinity, the exponential part of the function will tend asymptotically to zero.
Now, if we want to have an horizontal asymptote at y = -2, then we also need to have a constant term equal to -2 which takes weight as x tends to infinity, and the other part of the function becomes almost zero.
So the function will be something like:
f(x) = 2^(-x) - 2
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