We present table-driven algorithms for computing interval bounds on several common elementary functions. Our algorithms use directed rounding to obtain sharp bounds---within 1.5 units in the last place of the exact range of the function over the argument interval---without the explicit use of extended precision. Moreover, by performing all floating point operations in the same rounding mode, our algorithms can exploit software pipelining to provide better performance than simply evaluating the corresponding point elementary function at each endpoint of the argument interval and rounding.