Given an odd function, which of the following transformations would result in an odd function? Check all that apply.horizontal translationreflection across the x-axisvertical stretchvertical translation

An odd function satisfies f(-x) = -f(x). Reflecting across the x-axis changes it to -f(x), which still satisfies the odd-function rule; multiplying the function by a constant in a vertical stretch also preserves that rule. A horizontal translation generally moves the graph away from the origin, and a nonzero vertical translation breaks the symmetry about the origin.

AI-written and checked against the verified answer.