Question 6 Consider the function \( y=\sqrt{4-x} \). What are the domain and range of this function? domain: \( x \leq 4 \), range: \( y \geq 0 \) domain: \( x \leq 2 \), range: \( y \geq 2 \) domain: \( x \geq 2 \), range: \( y \geq 2 \) domain: \( x \geq 4 \), range: \( y \geq 0 \)

The function \( y=\sqrt{4-x} \) has its domain defined by the condition inside the square root being non-negative. This leads us to \( 4 - x \geq 0 \), which simplifies to \( x \leq 4 \). Therefore, the domain is all real numbers less than or equal to 4. As for the range, since the square root function only outputs non-negative values, the minimum value of \( y \) is 0 (when \( x = 4 \)), and it can increase indefinitely as \( x \) approaches negative infinity. Thus, the range is \( y \geq 0 \). To double-check, always evaluate \( y \) at critical points; for this function, \( y(4) = 0 \) is our starting point. As \( x \) decreases, \( y \) grows larger, emphasizing that the function can capture all positive \( y \) values as \( x \) moves leftward, confirming that \( y \) ranges from \( 0 \) to \( +\infty \). Keep an eye on those square roots—they can be tricksters with their domains!