Which of the following is an even function? g(x) = (x – 1)2 + 1 g(x) = 2x2 + 1 g(x) = 4x + 2 g(x) = 2x

I assume the 2s after the x - 1 and x in the first two functions are actually exponents.  

g(x) = (x - 1)^2 + 1 = x^2 - 2x + 2. g(-x) = (-x - 1)^2 + 1 = x^2 + 2x + 1 + 1 = x^2 + 2x + 2. NEITHER.  

g(x) = 2x^2 + 1; g(-x) = 2(-x)^2 + 1 = 2x^2 + 1. Since g(-x) = g(x), this is EVEN.  

g(x) = 4x + 2; g(-x) = -4x + 2. NEITHER.  

g(x) = 2x; g(-x) = -2x. Since g(-x) = -g(x), this is ODD

Step-by-step explanation:

g(x) = 2x2 + 1

Step-by-step explanation:

x^2 is an even function

g(x) = (x – 1)^2 + 1   since this is translated to the left and up.  Translation to the left or right make it lose its parity. It is not even

g(x) = 2x^2 + 1 This is only translated up  so it is still even

x is an odd function

g(x) = 4x + 2   This is shifted up  its is still an odd function

g(x) = 2x  This is still an odd function

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step-by-step explanation:

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the correct answer is 5 6 and 7