Find the vertical asymptotes of f(x) = (2x + 7) divided by (x squared - 4x).

1. Vertical asymptotes come from denominator factors that do not cancel with the numerator. 2. Factor the denominator as x times (x - 4). 3. Setting each factor to zero gives x equal to 0 and x equal to 4. 4. Check the numerator at each value so that neither is a shared factor. 5. At x equal to 0 the numerator is 7, and at x equal to 4 it is 15, so neither cancels. 6. Both values therefore give vertical asymptotes. 7. The pair x = 0 and x = -4 misreads the factor (x - 4) as (x + 4). 8. The pair x = 2 and x = 7 solves the numerator instead, which locates an x-intercept. 9. The pair x = 2 and x = -2 treats the denominator as x squared minus 4 and loses the factor x. _Source: OpenStax Precalculus (CC BY 4.0), section 3.7 Rational Functions_