The function g(x) = 3x3 + x is an odd function. Which transformations of g(x) would result in odd functions? Check all that apply.–g(x)g(2x)g(x − 1)g(x) − 3g(–x)

An odd function satisfies f(−x) = −f(x). Negating g(x) keeps it odd, and replacing x with 2x also preserves oddness because g(−2x) = −g(2x). Likewise, g(−x) = −g(x), which is still odd. The shifts g(x − 1) and g(x) − 3 are not odd in general because shifting the graph horizontally or vertically breaks the odd-function symmetry.

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