If f : R −→ R is continuous and f (7) > 2, then ∃δ > 0 such that .... If f : R −→ R is continuous and f (7) > 2, then ∃δ > 0 such that f (x) > 2 ∀x ∈ Vδ (7). I know the definition of continuous at a point. However, the question does not specific any particular point. Will it still work? Could anyone help get me started? What I got so far For all epsilon > 0 there exist δ > 0 such that whenever x in R and |x-7|< δ, it follow that |f(x) - f(7)| < |f(x) - 2|< sth that I am not sure Am I going the right direction?