This comes fromCalculus with Analytic Geometryby Purcell and Varberg, fifth edition, section 2.8, chapter review true/false quiz #28.

If f(x) < 10 for all x, and limit as x-> 2 of f(x) exists then limit as x->2 of f(x) < 10.

I answered true because either the function is continuous and f(2) < 10 from the first condition or it is discontinuous and all function values of f(x) near x=2 are less than 10.

The answer key disagrees. What did I miss?