1. **Problem Statement:** Find the absolute maximum and absolute minimum values of the function $y=f(x)$ from the given graph. 2. **Understanding the terms:** - The **absolute maximum** is the highest point on the entire graph. - The **absolute minimum** is the lowest point on the entire graph. - A **local maximum** is a point where the function value is higher than all nearby points. - A **local minimum** is a point where the function value is lower than all nearby points. 3. **From the graph description:** - The function starts near $(-4,0)$ and ends beyond $(4,8)$. - There is a local minimum at $(0,0)$. - There is a local maximum at approximately $(2,6)$. 4. **Absolute maximum:** - Since the graph continues increasing beyond $x=4$ and reaches $y=8$ there, and no higher point is mentioned, the absolute maximum is at $x=4$ with $f(4)=8$. 5. **Absolute minimum:** - The lowest point on the graph is the local minimum at $(0,0)$. - No points lower than $0$ are described, so the absolute minimum is $f(0)=0$. 6. **Local extrema:** - Local minimum at $x=0$ with value $0$. - Local maximum at $x=2$ with value $6$. **Final answers:** - Absolute maximum: $f(4)=8$ - Absolute minimum: $f(0)=0$ - Local maximum: $f(2)=6$ - Local minimum: $f(0)=0$