the entire graph of the function g is shown in the figure below.\nwrite the domain and range of g using…

Explanation:

Step1: Determine the domain

The domain of a function is the set of all x - values for which the function is defined. Looking at the graph, the leftmost point (excluding the open circle) has an x - value of - 2 (but since it's an open circle, we don't include - 2), and the rightmost point has an x - value of 2 (and it's a closed dot, so we include 2). So the domain is from - 2 (not included) to 2 (included), which in interval notation is $(-2,2]$.

Step2: Determine the range

The range of a function is the set of all y - values the function takes. Looking at the graph, the lowest y - value (from the open circle) is - 4 (but since it's an open circle, we don't include - 4), and the highest y - value is 5 (and it's a closed dot, so we include 5). So the range is from - 4 (not included) to 5 (included), which in interval notation is $(-4,5]$.

Answer:

domain: $(-2,2]$ range: $(-4,5]$