1. The problem asks whether the function $y = 2 \sin(x)$ is one-to-one. 2. A function is one-to-one (injective) if each output corresponds to exactly one input. 3. The sine function $\sin(x)$ is periodic with period $2\pi$, meaning it repeats values every $2\pi$ units. 4. Since $\sin(x)$ repeats values, $2 \sin(x)$ also repeats values and thus is not one-to-one over all real numbers. 5. For example, $\sin(0) = 0$ and $\sin(2\pi) = 0$, so $y=2\sin(0) = 0$ and $y=2\sin(2\pi) = 0$ but $0 \neq 2\pi$. 6. Therefore, the function $y = 2 \sin(x)$ is not one-to-one. Final answer: False