To find the horizontal asymptote of a function, we need to determine the limit of the function as x approaches positive or negative infinity.
For the given function f(x) = (2x^3 + 4)/(3x^3 - 1), we can see that the degree of the numerator (3) and the denominator (3) are equal. In such cases, we look at the ratio of the coefficients of the highest power term in the numerator and denominator.
The coefficient of the highest power term in the numerator is 2, and the coefficient of the highest power term in the denominator is 3. The ratio of these coefficients is 2/3.
As x approaches positive or negative infinity, the terms with lower powers become insignificant compared to the highest power terms. So, the function approaches the ratio of the coefficients, which is 2/3.
Therefore, the equation of the horizontal asymptote for f(x) is y = 2/3.
Option D: Y = 2/3.
find the equation of the horizontal asymptote for f(×). f(×)=2×^3+4/3×^3-1
A. No horizontal asymptote
B. Y=3
C. Y=0
D. Y=2/3
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