christiitoff
Answered

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

AIt is an even function.

BIt is an odd function.

CIt is both an even and an odd function.

DIt is neither an even nor an odd function.

Verified Answer :

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.

danielmaduroh

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:

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


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