Final Answer:
The function is not one-to-one because different inputs (x=1 and x=3) result in the same output (y=3).
Step-by-step explanation:
In mathematics, a one-to-one function is a function where distinct inputs have distinct outputs. In this case, since both x=1 and x=3 yield the same output y=3, the function is not one-to-one. A one-to-one function ensures that each input value corresponds to a unique output value, eliminating the possibility of two different inputs mapping to the same output.
To elaborate, a one-to-one function passes the horizontal line test, meaning that no horizontal line intersects the graph of the function more than once. In the given function, the outputs for x=1 and x=3 both being y=3 violate this condition, indicating a lack of one-to-one correspondence.
It implies that the function fails to preserve distinctness between inputs and outputs, as there exist different inputs producing identical results. This property can have implications in various mathematical applications, emphasizing the importance of understanding and identifying one-to-one functions.