Determine the equations of all of the asymptotes of the function: y=(2x+1)/(x-3)

## Step 1: Finding the Vertical Asymptote<br />### A vertical asymptote occurs when the denominator of a rational function is equal to zero and the numerator is not equal to zero at the same value of $x$. We set the denominator equal to zero and solve for $x$: $x - 3 = 0 \Rightarrow x = 3$. Since the numerator is not zero at $x=3$, this is a vertical asymptote.<br /><br />## Step 2: Finding the Horizontal Asymptote<br />### The degree of the numerator (1) is equal to the degree of the denominator (1). In this case, the horizontal asymptote is the ratio of the leading coefficients. The leading coefficient of the numerator is 2, and the leading coefficient of the denominator is 1. Thus, the horizontal asymptote is $y = \frac{2}{1} = 2$.