Using the provided graph of function g, determine its domain, evaluate g at specific points, and identify its local extrema.

The domain of a function refers to the set of all possible input values (x-values) for which the function is defined. From the given graph, the curve starts at $x=-4$ and ends at $x=4$. The function is continuous over this interval.

The domain of $g$ is $\boxed{[-4, 4]}$.

We read the corresponding y-values for each given x-value directly from the graph. Each small square on the grid represents 0.2 units.

• For $x=-4$, $g(-4) = 5$.
• For $x=-3$, $g(-3) = 0$.
• For $x=-2$, $g(-2) = -2.8$.
• For $x=-1$, $g(-1) = 0$.
• For $x=0$, $g(0) = 2.5$.
• For $x=1$, $g(1) = 5$.
• For $x=4$, $g(4) = -4$.

The values are:
$g(-4) = \boxed{5}$
$g(-3) = \boxed{0}$
$g(-2) = \boxed{-2.8}$
$g(-1) = \boxed{0}$
$g(0) = \boxed{2.5}$
$g(1) = \boxed{5}$
$g(4) = \boxed{-4}$

• a. A local maximum is a point where the function changes from increasing to decreasing, forming a "peak". From the graph, the function reaches a peak at $x=1$. The local maximum value of $g$ is $\boxed{5}$ (occurring at $x=1$).
• b. A local minimum is a point where the function changes from decreasing to increasing, forming a "valley". From the graph, the function reaches a valley at $x=-2$. The local minimum value of $g$ is $\boxed{-2.8}$ (occurring at $x=-2$).

The table of variations shows the intervals where the function is increasing or decreasing, along with the values at the critical points and endpoints.
The function decreases from $x=-4$ to $x=-2$.
The function increases from $x=-2$ to $x=1$.
The function decreases from $x=1$ to $x=4$.

The table of variations is: