Question

the entire graph of the function g is shown in the figure below. write the domain and range of g using interval notation. domain: range:

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 (open circle) is at \(x=-3\) and the rightmost point (open circle) is at \(x = 3\). Since the circles are open, we use parentheses. So the domain is the interval from \(-3\) to \(3\), not including the endpoints. So domain: \((-3,3)\)

Step2: Determine the range

The range of a function is the set of all y - values that the function takes. Looking at the graph, the highest y - value (at the left open circle) is \(y = 5\) and the lowest y - value (at the right open circle) is \(y=-5\). Since the function's graph goes from \(y = 5\) (not included, open circle) down to \(y=-5\) (not included, open circle), the range is the interval from \(-5\) to \(5\), not including the endpoints. So range: \((-5,5)\)

Answer:

domain: \((-3, 3)\)
range: \((-5, 5)\)