What is the range of this function? \[ y=-3|x| \] \[ \{y \mid y \geq 0\} \] \[ \{y \mid y \geq 3\} \] \[ \{y \mid y<0\} \] \[ \{y \mid y \leq 0\} \]

Step 1 ：The function given is a transformation of the absolute value function. The absolute value function always returns a non-negative value. However, the function is multiplied by -3, which means it will always return a non-negative value multiplied by -3, resulting in a non-positive value.

Step 2 ：Therefore, the range of the function should be all y such that y is less than or equal to 0.

Step 3 ：Final Answer: \(\boxed{\{y \mid y \leq 0\}}\)