hello

For which of the following functions is it true that -f(x)=f(-x) for all values of x?

A) f(x)=x+4

B) f(x)=x^2+4

C) f(x)=x^3+4

D) f(x)=x^2+x

E) f(x)=x^3+x

so does E become like -x^3-x(since we divide it by -1)=-x^3-x(since we plug in -1?) Thank you

What you need in this question is for the function to be symmetrical about the origin: –*f*(*x*) = *f*(–*x*) is the definition of an odd function. Graph all of the choices and you’ll see that only choice E is symmetrical about the origin.

The other way to get this is by elimination. Any choice with a constant in it (A, B, and C) can’t be right. D can’t be right because of the *x*^2 part—(–2)^2 ≠ –(2^2).