Find the domain and range of the relation and determine whether it is a function.
A. domain: x > 1; range: y > 0; Yes, it is a function.
B. domain: all real numbers; range: all real numbers; Yes, it is a function.
C. domain: positive integers; range: positive integers; No, it is not a function.
D. domain: x ≥ 0; range: y >1; No, it is not a function.
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Notice the curve gets closer and closer to x = 1, but never quite becomes x = 1. As x becomes larger, it keeps going forever. That shows a domain of x > 0.
Now look at it for y in a similar way as I did for x to find the range.
Finally, the question of if it is a function can be answered by the vertical line test.
If you look at the graph of a relation, and you want to know if it is a function, think of a vertical line moving horizontally from left to right. If the line ever touches more than one point on the graph at once, it is not a function. If the relation is a function, the vertical line only touches one point of the curve at a time.