Answer:
41) Yes, the relation is a function.
42) The domain of the function is [-2, 4].
43) The range of the function is [-1, 3].
Explanation:
Relations and Functions
A relation is a set of ordered pairs where each input (x-value) is associated with one or more outputs (y-values).
A function is a special type of relation where each input (x-value) is associated with exactly one output (y-value).
We can determine if a graphed relation is a function by applying the Vertical Line Test. It states that if a vertical line intersects the graph at more than one point, then the relation does not pass the test and is not a valid function.
As the given graph passes the Vertical Line Test, the relation is a function.
Domain and Range
The domain of a function is the set of all possible input values (x-values).
The range of a function is the set of all possible output values (y-values).
From inspection of the given graph, the continuous curve begins in quadrant II at point (-2, 1) and ends in quadrant IV at point (4, -1).
The endpoints of the graph are represented by closed circles, which means that the corresponding x and y values are included in the domain and range.
Therefore, the domain of the function is the x-values of the endpoints: [-2, 4].
The minimum point of the curve is endpoint (4, -1) and the maximum point is (0, 3). Therefore, the range of the function is the y-values of the minimum and maximum points: [-1, 3].