Final answer:
The horizontal asymptote of the exponential function y = a.bˠ is y = 0, assuming b > 0 and b != 1. This is because as x approaches infinity, the term bˠ grows larger for b > 1 or approaches zero for 0 < b < 1.
Step-by-step explanation:
The student has asked about the horizontal asymptote of the equation y = a.bˠ. The formula given seems to represent an exponential function, not a linear equation or a polynomial. In an exponential function of the form y = a ⋅ bˠ (where 'b' is the base and 'b' is not equal to 1), the horizontal asymptote can be determined by considering the limits as 'x' approaches infinity or negative infinity.
For b > 0, as x approaches infinity, assuming b != 1, the term bˠ grows larger if b > 1, or approaches zero if 0 < b < 1. As x approaches negative infinity, for b > 1, bˠ approaches zero. Thus, the horizontal asymptote is not dependent on the value of 'a' in the exponential function, but rather the properties of exponential growth or decay.
If b = 1, then the equation simplifies to y = a, which is a horizontal line, therefore the horizontal asymptote would be y = a. However, as the question presents an exponential function (implying b != 1), the correct answer for the horizontal asymptote of y = a.bˠ is y = 0.