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).

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