Thank you for the opportunity to help you with your question!
The domain is the set of
all first elements of ordered pairs (x-coordinates).
The range is the set of all
second elements of ordered pairs (y-coordinates).
The domain tells us all the x values that our function can be. To find these by looking at the graph, we look for x
values that the graph never touches. Ask yourself, at what points does
the graph jump? Well, the graph seems to jump or break apart at the
vertical asymptotes. So all the vertical asymptotes of our function tell
us what numbers are not part of our domain.
How to find Range
The range of a function is the spread of possible y-values (minimum y-value to maximum y-value)
Substitute different x-values into the expression for y to
see what is happening. (Ask yourself: Is y always positive? Always negative? Or maybe not equal to certain values?)
Make sure you look for minimum and maximum values of y.
Please let me know if you need any clarification. I'm always happy to answer your questions.