1. The problem statement, all variables and given/known data Both the following is true for a particular choice of function f(x): For any ε>0 there exists an N>0 such that x>N --> |f(x) - 2| < ε For any ε>0 there exists an N<0 such that x<N --> |f(x)| < ε Sketch the graph of the function that satisfies both of these conditions. There are infinitely many correct answers, you need to only sketch the graph of one of them. Hint: can you say anything about the asymptotes of f(x) 2. Relevant equations 3. The attempt at a solution I'm not sure but can it be assumed the y-axis (y=0) and y = 2 are horizontal asymptotes? And thus any graph sketched that stays in it those boundaries is acceptable .