Find the range of the function
\[k(x) = \frac{2x + 7}{x - 3}.\]
Set
\[y = \frac{2x + 7}{x - 3}.\]Solving for $x,$ we find
\[x = \frac{3y + 7}{y - 2}.\]Thus, for any value of $y,$ we can find a corresponding value of $x,$ except $y = 2.$  Therefore, the range of the function is $\boxed{(-\infty,2) \cup (2,\infty)}.$