Question

If the parent function f(x) = x2 is modified to g(x) = 2x2 + 1, which statement is true about g(x)?

A. It is an even function.

B. It is an odd function.

C. It is both an even and an odd function.

D. It is neither an even nor an odd function.

Answer 1

If f(-x) = -f(x) that the function is odd. If  f(-x)=f(x) then the function is even.

g(-x) = 2(-x)^2+1 = 2x^2+1 = g(x). The function is even.
The answer to your question is A.
I hope that this is the answer that you were looking for and it has helped you.

Answer 2

The right answer is A. It is an even function.

A function is said to be even if its graph is symmetric with respect to the $y-axis$, that is:

$y=f(x) \ is \ \mathbf{even} \ if, \ for \ each \ x \ in \ the \ domain \ of \ f:\\ \\ f(-x)=f(x)$

Since:

$g(x)=2x^2+1 \ and \\ \\ g(-x)=2(-x)^2+1 \therefore g(-x)=2x^2+1 \\ \\ \therefore \boxed{g(x)=g(-x)}$