Answer:
No, a non-complex equation cannot have 2 horizontal asymptotes. By definition, a horizontal asymptote is a horizontal line that the function approaches as x goes to positive or negative infinity. If there were two horizontal asymptotes, the function would have to approach two different horizontal lines as x goes to infinity, which is not possible for a single-valued function.
Similarly, a non-complex equation cannot have 2 vertical asymptotes. A vertical asymptote is a vertical line where the function approaches infinity or negative infinity as x approaches the line from either side. If there were two vertical asymptotes, the function would have to approach infinity or negative infinity as x approaches each line, which is not possible for a single-valued function.
Using a complex number as x does not change the behavior of asymptotes. If a function has a vertical asymptote at a real number, it will still have a vertical asymptote at that number when x is a complex number. Similarly, if a function has a horizontal asymptote, it will still have a horizontal asymptote when x is a complex number.
However, if a function has a vertical asymptote at a complex number, it may behave differently depending on the direction in which x approaches the asymptote. If the function approaches different values as x approaches the asymptote from different directions, then the function may not have a limit at the complex number and may not have a vertical asymptote. Similarly, if a function has a horizontal asymptote and is not defined for complex values of x, then it may not have a limit at infinity and may not have a horizontal asymptote.
Explanation: