from the graph of the function, state the domain, the range, and the intervals on which the function is…

Explanation:

Step1: Identify domain from graph

The domain is the set of all x - values for which the function is defined. Looking at the graph of part (a), the left - most x - value is (x=-3) and the right - most x - value is (x = 3). So the domain is ([-3,3]).

Step2: Identify range from graph

For part (a), the lowest y - value is (y = 0) (at the bottom of the semi - circle) and the highest y - value is (y=3) (at the top of the semi - circle). So the range is ([0,3]).

Step3: Determine increasing intervals

A function is increasing when as (x) increases, (y) also increases. For part (a), the function is increasing on the interval ([-3,0]).

Step4: Determine decreasing intervals

A function is decreasing when as (x) increases, (y) decreases. For part (a), the function is decreasing on the interval ([0,3]).

Step5: Check for constant intervals

There are no intervals where the function is constant (where (y) does not change as (x) changes) for part (a).

For part (b), assume the function is a single point at ((2,2)):

• Domain: ({2}) (a single x - value)
• Range: ({2}) (a single y - value)
• There are no increasing, decreasing or constant intervals as it is just a single point.

Answer:

(a) Domain: ([-3,3]), Range: ([0,3]), Increasing interval: ([-3,0]), Decreasing interval: ([0,3]), Constant interval: None (b) Domain: ({2}), Range: ({2}), Increasing interval: None, Decreasing interval: None, Constant interval: None