1. use the following graph to find the following.\n(a) domain and range\n(b) intervals of increase and…

Explanation:

Step1: Identify domain from x - values

The graph extends from (x=-2) to (x = 3). So the domain is ([-2,3]).

Step2: Identify range from y - values

The lowest (y) - value is approximately (y=-3) and the highest is (y = 7). So the range is ([-3,7]).

Step3: Determine intervals of increase

The function is increasing where the graph goes up as we move from left to right. This is on the intervals ([-2,0]) and ([2,3]).

Step4: Determine intervals of decrease

The function is decreasing where the graph goes down as we move from left to right. This is on the interval ([0,2]).

Step5: Find local maxima

Local maxima occur where the function changes from increasing to decreasing. At (x = 0), (y = 2) is a local maximum.

Step6: Find local minima

Local minima occur where the function changes from decreasing to increasing. At (x=2), (y=-3) is a local minimum.

Answer:

(a) Domain: ([-2,3]), Range: ([-3,7]) (b) Intervals of increase: ([-2,0]\cup[2,3]), Intervals of decrease: ([0,2]) (c) Local maximum: ((0,2)), Local minimum: ((2,-3))