find the horizontal asymptotes. f(x) = (3x³ + 5x² - 8x + 2)/(4x³ - 2x² + 6x - 1) o y = 3/4 o y = 3 o y = 4 o…

Explanation:

Step1: Identify degree of polynomials

The degree of the numerator $3x^{3}+5x^{2}-8x + 2$ and the denominator $4x^{3}-2x^{2}+6x - 1$ is $n = m=3$ (highest - power of $x$).

Step2: Use horizontal - asymptote rule

When $n = m$ (degree of numerator = degree of denominator) for a rational function $y=\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}$, the horizontal asymptote is $y=\frac{a_n}{b_m}$, where $a_n$ is the leading coefficient of the numerator and $b_m$ is the leading coefficient of the denominator. Here, $a_n = 3$ and $b_m = 4$, so $y=\frac{3}{4}$.

Answer:

A. $y=\frac{3}{4}$