Which of the following is an even function?

A. g (x) = (x - 1) 2 + 1

B. g (x) = 2x2 + 1

C. g (x) = 4x + 2

D. g (x) = 2x

The definition of an even function is g (-x) = g (x). In other words, x values of the same magnitude but different signs will produce the same y value. An easy way to recognize this is that the degree of the function is even (for polynomials) and the function is centered at x=0. A is not centered at 0, it is centered at 1. B is an even function because it has an even degree, and is centered at 0. C and D are not even functions because they have odd degrees. So B is the right answer.