Question

is the function f(x)=x^2+x+1 even odd or neither

Answer 1

neither

Answer 2

Can you briefly explain why it is neither

Answer 3

it is neither symmetric about origin nor about y-axis

Answer 4

a function is even if:

f(x) = f(-x)

or in other words, a function is even if it has the same value for x or -x

a function is odd if:
f(x) + f(-x) = 0

or in other words, a function if the function evaluated at -x gives the opposite value of the function evaluated at x

the function in your post is neither, because it doesn't fit the requirements.

Answer 5

for instance:

f(x)=x^2+x+1
f(1) = 1^2 + 1 + 1 = 3

f(-1) = 1 - 1 + 1 or 2

if it was even, f(1) would equal f(-1) [they would both be 3]

if it was odd, f(1) would be the oppsite of f(-1) [one is 3, the other is -3]

neither is the case here