Which of the following statements best describes the domain of the functions tan and arctan?
Tan domain is all real numbers; Arctan domain is all real numbers.
Tan domain is restricted; Arctan domain is all real numbers.
Tan domain is all real numbers; Arctan domain is restricted.
Tan domain is restricted; Arctan domain is restricted.
Look at the graphs I have attached. Arctan is the one that keeps going forever to the right and left. Tan is the one that goes forever up and down. Notice Tan doesn't continue forever to the right and left without jumping.
The domain concerns the numbers along the x-axis (right/left). If you try to trace Arctan with your finger, it's not interrupted in the way Tan is. Therefore, the domain of Tan is restricted while the domain of Arctan is all real numbers (you can keep zooming out on the graph and you'll be able to trace the ArcTan graph to the right and left without interruptions.
