Question: User: Part 4 of 8 Use the graph of the function. 21. Identify the domain and range of the function. 22. Identify the x- and y-intercepts of the function. 23. Determine over what interval the function is positive or negative. 24. Determine over what interval the function is increasing or decreasing. 22. Identify all x-intercepts. Select the correct choice below and fill in any answer boxes within your choice. A. The x-intercept(s) is(are) -5,3. (Type your answer(s) as integers or simplified fractions. Use a comma to separate answers as needed.) B. There are no x-intercepts. Identify all y-intercepts. Select the correct choice below, and fill in any answer boxes within your choice. A. The y-intercept(s) is(are) 4. (Type your answer(s) as integers or simplified fractions. Use a comma to separate answers as needed.) B. There are no y-intercepts. Graph shape and math (top-right): A piecewise linear graph with solid points at $(-5, 0)$, $(-1, 2)$, and $(5, -1)$, connected by straight line segments; it crosses the y-axis at $(0, 1)$ and the x-axis at $x = -5$ and $x = 3$.

1. **State the problem:** We analyze the given piecewise linear function with points $(-5,0)$, $(-1,2)$, $(5,-1)$, crossing the y-axis at $(0,1)$ and x-axis at $x=-5$ and $x=3$. 2. **Domain and Range:** - The domain is all $x$ values covered by the graph, from the leftmost to rightmost points. - The range is all $y$ values the function attains. 3. **Domain:** The graph extends from $x=-5$ to $x=5$, so domain is $$[-5,5].$$ 4. **Range:** The lowest $y$ value is $-1$ at $x=5$, highest is $2$ at $x=-1$, so range is $$[-1,2].$$ 5. **X-intercepts:** Points where $y=0$. - Given points $(-5,0)$ and the graph crosses $x=3$ on x-axis. - So x-intercepts are $$-5, 3.$$ 6. **Y-intercept:** Point where $x=0$. - Given as $(0,1)$, so y-intercept is $$1.$$ 7. **Intervals where function is positive or negative:** - Positive means $y>0$, negative means $y<0$. - From $x=-5$ to $x=0$, $y$ goes from $0$ to $1$ and up to $2$ at $x=-1$, so $y>0$ on $(-5,0]$ except at $x=-5$ where $y=0$. - From $x=0$ to $x=3$, $y$ decreases from $1$ to $0$, so $y>0$ on $(0,3)$. - From $x=3$ to $x=5$, $y$ goes from $0$ to $-1$, so $y<0$ on $(3,5]$. 8. **Intervals where function is increasing or decreasing:** - Increasing means $y$ rises as $x$ increases. - Decreasing means $y$ falls as $x$ increases. - From $x=-5$ to $x=-1$, $y$ rises from $0$ to $2$, so increasing on $[-5,-1]$. - From $x=-1$ to $x=5$, $y$ falls from $2$ to $-1$, so decreasing on $[-1,5]$. **Final answers:** - Domain: $$[-5,5]$$ - Range: $$[-1,2]$$ - X-intercepts: $$-5, 3$$ - Y-intercept: $$1$$ - Positive intervals: $$(-5,3)$$ - Negative intervals: $$(3,5]$$ - Increasing interval: $$[-5,-1]$$ - Decreasing interval: $$[-1,5]$$