Question: 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) . (Type your answer(s) as integers or simplified fractions. Use a comma to separate answers as needed.) B. There are no y-intercepts. Graph: a piecewise linear graph in the center-right with red points connected by line segments through approximately (-5,0), (-1,2), and (5,-1); the graph crosses the x-axis at about x = -5 and x = 3. position_hint = center

1. **Problem Statement:** Identify the domain, range, x- and y-intercepts, intervals where the function is positive/negative, and intervals where it is increasing/decreasing from the given piecewise linear graph. 2. **Domain:** The domain is the set of all x-values for which the function is defined. From the graph, the function has points from about $x = -5$ to $x = 5$. So, the domain is $$[-5, 5].$$ 3. **Range:** The range is the set of all y-values the function takes. From the graph, the lowest y-value is about $-1$ at $x=5$, and the highest y-value is about $2$ at $x=-1$. So, the range is $$[-1, 2].$$ 4. **X-intercepts:** These are points where the graph crosses the x-axis ($y=0$). From the graph, the function crosses the x-axis at approximately $x = -5$ and $x = 3$. Therefore, the x-intercepts are $$-5, 3.$$ 5. **Y-intercept:** This is the point where the graph crosses the y-axis ($x=0$). From the graph, the function does not cross the y-axis at $x=0$ (no point shown at $x=0$), so there is no y-intercept. Therefore, there are no y-intercepts. 6. **Intervals where the function is positive or negative:** - Positive means $y > 0$. - Negative means $y < 0$. From the graph: - The function is positive between $x = -5$ and $x = 3$ where the graph is above the x-axis. - The function is negative between $x = 3$ and $x = 5$ where the graph is below the x-axis. So, positive interval: $$(-5, 3)$$ Negative interval: $$(3, 5)$$ 7. **Intervals where the function is increasing or decreasing:** - Increasing means the function values go up as $x$ increases. - Decreasing means the function values go down as $x$ increases. From the graph: - From $x = -5$ to $x = -1$, the function increases from $0$ to $2$. - From $x = -1$ to $x = 5$, the function decreases from $2$ to $-1$. So, increasing interval: $$[-5, -1]$$ Decreasing interval: $$[-1, 5]$$