4. for the function graphed here, determine its absolute maximum and absolute minimum on the following…

Explanation:

Step1: Analyze interval (-3, -0.5)

By observing the graph, in the open - interval $(-3,-0.5)$, the function is increasing. The maximum value in this interval does not exist as it is an open interval. The minimum value occurs near $x=-3$ and $y\approx - 1$.

Step2: Analyze interval [0, 2)

In the half - open interval $[0,2)$, the function first increases and then starts to decrease. The maximum value is $y = 2$ which occurs at $x = 1$. The minimum value is $y = 1$ which occurs at $x = 0$.

Step3: Analyze interval (0, 3)

In the open interval $(0,3)$, the maximum value is $y = 2$ which occurs at $x = 1$. The minimum value occurs near $x = 3$ and $y\approx0$.

Step4: Analyze interval (-2, 0]

In the half - open interval $(-2,0]$, the function is increasing. The maximum value is $y = 1$ which occurs at $x = 0$. The minimum value occurs near $x=-2$ and $y\approx - 1$.

Answer:

(a) Maximum does not exist, minimum: $x\approx - 3,y\approx - 1$ (b) Maximum: $x = 1,y = 2$, minimum: $x = 0,y = 1$ (c) Maximum: $x = 1,y = 2$, minimum: $x\approx3,y\approx0$ (d) Maximum: $x = 0,y = 1$, minimum: $x\approx - 2,y\approx - 1$