1. The problem asks us to find the interval where the function is decreasing. 2. The function is piecewise linear through the points $(-6,0)$, $(-5,5)$, $(-2,5)$, $(0,4)$, $(1,3)$, $(2,1)$, and $(6,3)$. 3. To determine where the function is decreasing, we look at the slope between consecutive points. A function decreases where the slope is negative. 4. Calculate slopes between points: - Between $(-6,0)$ and $(-5,5)$: slope = $\frac{5-0}{-5+6} = \frac{5}{1} = 5$ (increasing) - Between $(-5,5)$ and $(-2,5)$: slope = $\frac{5-5}{-2+5} = 0$ (constant) - Between $(-2,5)$ and $(0,4)$: slope = $\frac{4-5}{0+2} = \frac{-1}{2} = -0.5$ (decreasing) - Between $(0,4)$ and $(1,3)$: slope = $\frac{3-4}{1-0} = -1$ (decreasing) - Between $(1,3)$ and $(2,1)$: slope = $\frac{1-3}{2-1} = -2$ (decreasing) - Between $(2,1)$ and $(6,3)$: slope = $\frac{3-1}{6-2} = \frac{2}{4} = 0.5$ (increasing) 5. The function decreases on the interval where the slope is negative, which is from $x = -2$ to $x = 2$. 6. Therefore, the function is decreasing on the interval $$-2 < x < 2$$. Final answer: The function decreases on the interval $-2 < x < 2$.