1. The problem statement, all variables and given/known data List all the asymptotes of f(x) = |x| / x 2. Relevant equations 3. The attempt at a solution This is a problem on a limits test in a Calculus AB class. I tried vertical asymptotes and horizontal asymptotes by setting the numerator and denominator equal to 0 but only getting x=0 |x|=0 x=0 Unfortunately that wasn't the answer to the question, but I plugged the equation in the calculator and it did appear to have a vertical asymptote at x=0 and two horizontal asymptotes at x=1 and x=-1 However I don't know how to find that algebraically. I did some research and saw an example where they found the limit of a function as it went to positive and negative infinity in order to find the asymptotes. I tried that: lim |x|/x = 1 x→∞ lim |x|/x = -1 x→-∞ At the end of this I was left with x=0 (from my very first attempt) x=1 x=-1 Questions 1. Is setting finding the limit of the function as it goes to infinity a solid way of finding asymptotes? 2. a. Is my final answer correct? b. If not, Could someone explain the mistakes/false-reasoning I made or lead me in the right direction?