  We examine the reliability of the tip of the red giant branch (TRGB) as a
distance indicator for stellar populations with different star formation
histories (SFHs) when photometric errors and completeness corrections at the
TRGB are small. In general, the TRGB-distance method is insensitive to the
shape of the SFH except when it produces a stellar population with a
significant component undergoing the red giant branch phase transition. The
I-band absolute magnitude of the TRGB for the middle and late stages of this
transition (~1.3-1.7 Gyr) is several tenths of a magnitude fainter than the
canonical value of M_I ~ -4.0. If more than 30% of all stars formed over the
lifetime of the Universe are formed at these ages, then the distance could be
overestimated by 10-25%. Similarly, the TRGB-distance method is insensitive to
the metallicity distribution of stars formed except when the average
metallicity is greater than <[Fe/H]> = -0.3. If more than ~70% of all stars
formed have [Fe/H] > -0.3, the distance could be overestimated by ~10-45%. We
find that two observable quantities, the height of the discontinuity in the
luminosity function at the TRGB and the median (V-I)_0 at M_I = -3.5 can be
used to test if the aforementioned age and metallicity conditions are met.
