how to determine if something is a function besides the statement "x's cannot repeat"
No idea what you mean by "x's cannot repeat"
The definition of a function is found in every textbook that deals with that topic
I don't get it when you said "x's cannot repeat"
To determine if something is a function, besides the statement "x's cannot repeat," you can follow these steps:
1. Identify the domain and range: The domain is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values). Take a look at the given data or equation to determine the values of x that are valid inputs and the corresponding y-values.
2. Check for uniqueness: For each value of x in the domain, make sure there is only one corresponding value of y in the range. In other words, no x-value should have multiple y-values associated with it. If there are any repetitions in the pairs of x and y values, then it is not a function.
3. Graph it: If you have a graph of the data or equation, you can visually check if there are any instances where a vertical line intersects the graph at more than one point. If there are multiple points of intersection, then it is not a function. This concept is known as the vertical line test.
4. Use the mapping rule: If you have a set of ordered pairs representing the relationship between x and y, you can check for repetitions in the x-values. If any x-value appears more than once, then it is not a function.
By following these steps, you can determine whether something is a function or not, even without relying solely on the statement "x's cannot repeat."