11 Determine the equation(s) of all the asymptotes of f(x)=(2x^2+1)/(3x^2)

## Step 1: Simplify the function<br />### We can rewrite the function $f(x) = \frac{2x^2 + 1}{3x^2}$ as $f(x) = \frac{2x^2}{3x^2} + \frac{1}{3x^2} = \frac{2}{3} + \frac{1}{3x^2}$.<br /><br />## Step 2: Find the Horizontal Asymptote<br />### As $x$ approaches infinity (positive or negative), the term $\frac{1}{3x^2}$ approaches 0. Therefore, the horizontal asymptote is $y = \frac{2}{3}$.<br /><br />## Step 3: Find the Vertical Asymptote<br />### The denominator $3x^2$ is equal to zero when $x=0$. Thus, there is a vertical asymptote at $x=0$.