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

Step 1: Determine the domain of definition of g. 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 [-4, 4]. Step 2: Determine the values of g(-4), g(-3), g(-2), g(-1), g(0), g(1) and g(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) = 5 g(-3) = 0 g(-2) = -2.8 g(-1) = 0 g(0) = 2.5 g(1) = 5 g(4) = -4 Step 3: Find the local maximum and local minimum of g. 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 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 -2.8 (occurring at x=-2). Step 4: Set up the table of variations of g. 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: |c|ccccccc| x & -4 & & -2 & & 1 & & 4 \\ Variation of g & 5 & & -2.8 & & 5 & & -4 \\ Send me the next one 📸