Final answer:
The function f(x)=x-√(4x²-3x²) simplifies to f(x)=0, revealing a horizontal asymptote at y=0. There are no vertical asymptotes for this specific function as it is not a rational function with denominators that could become undefined.
Step-by-step explanation:
To find horizontal and vertical asymptotes for the function f(x)=x-√(4x²-3x²), we need to simplify the function first. Since the square root of 4x²-3x² simplifies to x, our function becomes f(x)=x-x, which simplifies further to f(x)=0. Therefore, the horizontal asymptote is y=0 since the value of f(x) is constantly 0 regardless of x.
For vertical asymptotes, we look for values of x that would make the denominator of a rational function undefined, typically when a division by zero would occur. However, since our function is not a rational function, there are no vertical asymptotes based solely on its algebraic form. None of the given answer choices correctly match a vertical asymptote for this function. Thus, the closest correct answer would be (a) Horizontal asymptote: y=0, and no vertical asymptote implied by option x=0 would not apply here.