Thank you for the opportunity to help you with your question!
Domain is the range of x - values of the graph. Here the graph extends indefinitely on both ends. So the domain is ( - infinity, infinity ).
Range is the range of y - values of the graph. Here the lowest point on the graph is (0, -2). Hence the lowest y value is -2. Since there is no highest point on the graph, the range is [ -2, infinity).
Yes, the graph is a function because it passes the vertical line test. When you draw a vertical line, it passes through the graph only once.
Please let me know if you need any clarification. I'm always happy to answer your questions.