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

Even functions are symmetric about the x axis
basically, if you replace x with -x, the function won't changeso if g(-x)=g(x), then g(x) is even

replace x with -x and see if they are the same function

g(x)=(x-1)²+1replaceg(-x)=(-x-1)²+1g(-x)=((-1)(x+1))²+1g(-x)=(-1)²(x+1)²+1g(-x)=(1)(x+1)²+1g(-x)=(x+1)²+1
g(-x)=g(x)?(x+1)²+1=(x-1)²+1?(x+1)²=(x-1)²?nope, not

2nd oneg(x)=2x²+1g(-x)=2(-x)²+1g(-x)=2((-1)(x))²+1g(-x)=2((-1)²(x)²)+1g(-x)=2((1)(x²))+1g(-x)=2x²+1
g(-x)=g(x)?
2x²+1=2x²+1?truethis is an even function

g(x)=4x+2g(-x)=4(-x)+2g(-x)=4((-1)(x))+2g(-x)=-4x+2
g(-x)=g(x)?
-4x+2=4x+2?
false

g(x)=2xg(-x)=2(-x)
g(-x)=2(-1)(x)g(-x)=-2x
g(-x)=g(x)?-2x=2x?false

answer is is an even function