Explain what effect an economic slowdown (recession) in an economy
will have on the foreign exchange market?

If the recession causes "THE FED" to keep the discount rate low or
make it even lower, foreign investors will withdrtaw funds in the U.
S. to seek higher rates overseas.  Money will  become scarce in the U.
S.  This is happening now at a more than usual accelerated rate due to
the crisis of confidence in American business corporations. The longer
the crisis continues the more scarce money from overseas will become. 
Counter to these factors is the general improvement in basic economic
indicators.  If these are not undermined by the confidence crisis the
affect might not be that great.  It depends how quickly the public can
be educated by the politicians and the corporations.  Euros look like
a good buy right now!