Answer:
Domain: All real numbers
Range: f(x) ≥ 5 or f(x) < 2
Explanation:
The given graph is a graph of a piecewise function.
Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.
When graphing piecewise functions:
- An open circle is used where the value is not included in the interval.
- A closed circle is used where the value is included in the interval.
- An arrow is used to show that the function continues indefinitely.
Domain
The domain of a function is the set of all possible input values (x-values).
From inspection of the graph, the arrows show that the function continues indefinitely in both the positive and negative directions.
The value of x = 1 is not included in the left part of the graph, but it is included in the right part of the graph.
Therefore, the domain of the function is all real values of x:
Range
The range of a function is the set of all possible output values (y-values).
From inspection of the graph, there is an open circle at y = 2 and a closed circle at y = 5. Therefore, there are no y-values in the interval:
2 ≤ y < 5.
Therefore, the range of the function is f(x) < 2 or f(x) ≥ 5: