  This is an expository paper on approximating functions from general Hilbert
or Banach spaces in the worst case, average case and randomized settings with
error measured in the $L_p$ sense. We define the power function as the ratio
between the best rate of convergence of algorithms that use function values
over the best rate of convergence of algorithms that use arbitrary linear
functionals for a worst possible Hilbert or Banach space for which the problem
of approximating functions is well defined. Obviously, the power function takes
values at most one. If these values are one or close to one than the power of
function values is the same or almost the same as the power of arbitrary linear
functionals. We summarize and supply a few new estimates on the power function.
We also indicate eight open problems related to the power function since this
function has not yet been studied for many cases. We believe that the open
problems will be of interest to a general audience of mathematicians.
