For this problem, we are given the following rational function:
[tex]f(x)=\frac{4x^3+6x}{3x^3-2x+1}[/tex]
We need to determine the horizontal asymptote for this function. In order to determine this, we need to calculate the limit of the function when x approaches infinity. We have:
[tex]\lim_{x\rightarrow\infty}\frac{4(\infty)^3+6\cdot\infty}{3(\infty)^3-2\cdot\infty+1}=\frac{4}{3}[/tex]
The horizontal asymptote exists at y= 4/3. The correct option is C.
