Final answer:
The equation of the asymptote for the function f(x) = 4/(x²)² is y = 0. This is due to the function being a rational function with the degree of the polynomial in the denominator higher than the numerator. The correct answer is a) y = 0.
Step-by-step explanation:
The equation of the asymptote for the function f(x) = 4/(x²)² is y = 0. An asymptote is a line that the graph of a function approaches but never touches. Horizontal asymptotes occur in rational functions where the degree of the polynomial in the denominator is greater than the degree of the polynomial in the numerator.
Since the function is a rational function with a higher-degree polynomial in the denominator, there will be a horizontal asymptote at y = 0, because as x approaches infinity, the value of f(x) approaches zero.
A horizontal asymptote is a straight line that the function approaches as the independent variable (usually denoted as
�
x) tends to positive or negative infinity.
For instance, in the function
�
=
1
�
y=
x
1
, as
�
x approaches infinity or negative infinity,
�
y approaches
0
0. Hence, the line
�
=
0
y=0 is a horizontal asymptote.