1. The problem is to create a rational function similar to the example given: $$f(x) = \frac{2}{x^{2} - 64}$$ which factors as $$(x+8)(x-8)$$ and has vertical asymptotes at $x = -8$ and $x = 8$. 2. To create a similar function, choose a denominator that factors into two linear terms with distinct roots, for example, $x^{2} - 25 = (x+5)(x-5)$. 3. The numerator can be any constant or polynomial; to keep it simple, use a constant like 3. 4. Thus, the new function is: $$g(x) = \frac{3}{x^{2} - 25} = \frac{3}{(x+5)(x-5)}$$ 5. This function has vertical asymptotes at $x = -5$ and $x = 5$, similar to the original function's asymptotes at $x = -8$ and $x = 8$. 6. The domain excludes $x = -5$ and $x = 5$ because the denominator is zero at these points. Final answer: $$g(x) = \frac{3}{x^{2} - 25}$$