Final answer:
None of the options provided are exponential functions with a horizontal asymptote at y = 3. There might be a typo or misunderstanding in the question, as the standard form of an exponential function with a horizontal asymptote is not represented by any of the given choices.
Step-by-step explanation:
The question at hand is asking which exponential function has a horizontal asymptote at y = 3. In general, the horizontal asymptote of an exponential function occurs at the value that the function approaches as x goes to positive or negative infinity. In the given options, the only function that could potentially have a horizontal asymptote is a function that approaches a certain y value as x increases without bound. Therefore, we need to analyze each option to determine its behavior:
- f(x) = –3x 3: This is not a standard form for an exponential function.
- f(x) = –3x – 3: As x goes to infinity, the exponential term –3x goes to 0, and the function approaches -3.
- f(x) = 3(–x3): This is a polynomial function, not an exponential one, so it has no horizontal asymptote at y = 3.
- f(x) = 3(–x – 3): Similar to the previous option, this is a linear function with a negative slope, and it also does not have a horizontal asymptote at y = 3.
None of the provided options is an exponential function with a horizontal asymptote at y = 3. It seems there might have been a misunderstanding or typo in the question. If the question intended to refer to a standard form of an exponential function, typical representations are f(x) = abx + c, where c would be the horizontal asymptote if b is a positive real number not equal to 1. In such case, none of the given options match this form.