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If -3 < f < 4 and -2 < g < 1,then what is the range of possible values of fg.
f is defined for these values:
---------o===========================o--------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
g is defined for these values:
-------------o===========o--------------------
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
When f is very near -3 and g is very near -2, their product
fg is very near +6, so +6 is the least upper bound.
When f is very near 4 and g is very near -2, their product
fg is very near -8, so -8 is the greatest lower bound.
Therefore:
-8 < fg < 6
Edwin
