The domain is (–∞, 0). The function is undefined at x=0 and the correct option is D.
The domain of a function is the set of all possible input values for that function. In the case of a graph, the domain is all the possible x-values for which the graph has a defined y-value.
The graph in the image shows a function that is defined for all x-values less than zero. The function is not defined at x=0 because the graph has a hole at that point. Therefore, the domain of the function is (–∞, 0).
Another way to think about it is that the domain of the function is all the x-values for which the output of the function is real. The range of the function is the set of all possible output values. The range of the function in the image is all real numbers, including zero. However, the function is not defined at x=0, so it cannot output zero. Therefore, the domain of the function is (–∞, 0).
Here is a summary of the steps to find the domain of a function graph:
Look for any holes or gaps in the graph.
Look for any vertical asymptotes.
Consider the range of the function.
If the graph has any holes or gaps, then the domain is all the x-values except for the x-values at the holes or gaps.
If the graph has any vertical asymptotes, then the domain is all the x-values except for the x-values at the vertical asymptotes.
The range of the function can also help to determine the domain. For example, if the range of the function is all positive numbers, then the domain cannot include any negative numbers.
In the case of the graph in the image, there are no holes or gaps in the graph, and there are no vertical asymptotes. The range of the function is all real numbers, including zero. However, the function is not defined at x=0, so the domain of the function is (–∞, 0).
Therefore, the correct option is D.