To determine the domain and range of a graph, you need to examine the shape and behavior of the graph.
The domain of a graph is the set of all possible input values (often represented by "x") for which the graph is defined. This can typically be determined by examining the horizontal extent of the graph. For example, if the graph is a straight line that extends infinitely in both directions, then the domain is all real numbers.
The range of a graph is the set of all possible output values (often represented by "y") that the graph can produce. This can typically be determined by examining the vertical extent of the graph. For example, if the graph is a parabola that opens upwards and has a vertex at (0,0), then the range is all non-negative real numbers.
In some cases, the domain and range of a graph may be limited by specific features of the graph. For example, if the graph has a "hole" at a particular point, then that point is excluded from the domain. Similarly, if the graph has a vertical asymptote at a particular point, then the range is limited to either all positive or all negative numbers, depending on the direction of the asymptote.
Overall, determining the domain and range of a graph requires careful observation and analysis of its features and behavior.
