Question

Even function neither even nor odd odd function both even and odd F(X)=X2+3

Answer 1

For a function to be even, it must be symmetrical to the y-axis.

Although we have f(x) = x² + 3, let's just imagine the parent graph

f(x) = x² which has a y-intercept of 0 and is of average width.

This is symmetrical about the y-axis, but we want to know

whether or not f(x) = x² + 3 is symmetrical to the y-axis.

We can shift the parent graph f(x) = x² by adding

a constant, 3, to give us f(x) = x² + 3.

Translating the parent up or down will always result

in an even function because it will always be symmetrical.

Answer 2

We have the following definitions:
A function is even if, for each x in the domain of f, f (- x) = f (x). The even functions have reflective symmetry through the y-axis.
A function is odd if, for each x in the domain of f, f (- x) = - f (x). The odd functions have rotational symmetry of 180º with respect to the origin.
We have then:
F (-X) = (- X) 2 + 3
Rewriting:
F (-X) = (X) 2 + 3
F (-X) = F (X)
Answer:
F (-X) = F (X)
The function is even according to the definition: