For what values of \( x \) is \( y=-7-|x| \) increasing? decreasing? a increasing: not increasing on any interval; decreasing: \( (-7, \infty) \) o increasing: \( (0, \infty) \); decreasing: \( (-\infty, 0) \) o increasing: \( (-7, \infty) \); decreasing: not decreasing on any interval d increasing: \( (-\infty, 0) \); decreasing: \( (0, \infty) \)

To determine where the function \( y = -7 - |x| \) is increasing or decreasing, we first need to analyze the behavior of the function based on the absolute value. The function \( |x| \) can be expressed as: - \( |x| = x \) when \( x \geq 0 \) - \( |x| = -x \) when \( x < 0 \) Thus, we can rewrite the function \( y \) in two pieces: 1. For \( x \geq 0 \): \[ y = -7 - x \] This is a linear function with a slope of -1, which means it is decreasing for \( x \geq 0 \). 2. For \( x < 0 \): \[ y = -7 + x \] This is also a linear function, but with a slope of +1, which means it is increasing for \( x < 0 \). Now we can summarize the intervals of increase and decrease: - The function is **increasing** on the interval \( (-\infty, 0) \). - The function is **decreasing** on the interval \( (0, \infty) \). Thus, the correct answer is: - **Increasing**: \( (-\infty, 0) \); **Decreasing**: \( (0, \infty) \).