Final answer:
To find the horizontal asymptotes, check the highest power of x. For vertical asymptotes, check if the equation is undefined for any values of x.
Step-by-step explanation:
The given equation is y = 4x⁴ - x⁴.
To find the horizontal asymptotes, we need to observe the highest power of x in the equation. In this case, the highest power of x is 4. Since x⁴ goes to infinity as x approaches infinity and negative infinity as x approaches negative infinity, there are no horizontal asymptotes.
To find the vertical asymptotes, we need to check if there are any values of x for which the equation is undefined. In this case, the equation is defined for all real values of x. Therefore, there are no vertical asymptotes.