In a function, can you have the same x value, but different y values?
Example:
X Y
1 2
1 3
1 4
1 5
all the points lie on the same vertical line ----> not a function
Thanks! I was stuck on that question for a while!
Yes, in a mathematical function, it is possible to have the same x value but different y values. This means that for a given input x, the corresponding output y can be different.
Yes, in a function, it is possible to have the same x value but different y values. This is known as a one-to-many or many-to-one relationship. In mathematical terms, a function is defined as a relation where each input (x-value) is associated with exactly one output (y-value).
However, in the example you provided, it seems that the x value of 1 is associated with multiple y values (2, 3, 4, and 5). This violates the definition of a function because a specific input should only have one corresponding output.
To represent this data as a function, you could use a different approach. One option is to consider the x value along with another value (such as an index) to uniquely identify each pair. For example:
X Y
1a 2
1b 3
1c 4
1d 5
Here, the x values are differentiated by appending a unique identifier (such as a, b, c, d). This way, each pair has a unique identifier, and the relation can be considered a function.