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

Answer

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Answer

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

Steps

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: \(\boxed{\{y \mid y \leq 0\}}\)

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

Answer

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