1. The problem asks if the function $f(x) = 2x$ is positive for all values of $x$. 2. The function $f(x) = 2x$ is a linear function where the output depends on the value of $x$ multiplied by 2. 3. To determine if $f(x)$ is positive for all $x$, consider the sign of $x$: - If $x > 0$, then $2x > 0$. - If $x = 0$, then $2x = 0$ (not positive). - If $x < 0$, then $2x < 0$ (negative). 4. Since $f(x)$ is not positive for all $x$ (it is zero at $x=0$ and negative for $x<0$), the statement is false. Final answer: a. False