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A linear transformation is a function that preserves linear operations, such as addition and scalar multiplication. In this case, f(x) = 2x + 1 is a linear transformation because f(x + y) = 2(x + y) + 1 = 2x + 2y + 1 = f(x) + f(y) and f(cx) = 2(cx) + 1 = c(2x + 1) = cf(x) for any scalars c and vectors x and y.