Can a graph be one-to-one even if it isn't a function?
In the methods 3&4 textbook, there's a question where it gives a series of graphs and we have to basically define whether it is a function and whether it is one-to-one. There were some graphs however that satisfied the horizontal line test but did not satisfy the vertical line test. Even if these graphs satisfied the test to be one-to-one, the book says that they were not one-to-one as they weren't considered functions. Which raises the question whether a graph can be considered one-to-one even if it isn't a function.
For reference, the questions I'm referring to is in Exercise 1C, question 3 ii and v.
A graph is a set of (x, y) points satisfying some condition (typically, an equation involving x and y). Such a graph can satisfy the "horizontal line test", even though y is not a function of x – although, in this case, x is a function of y. (Rotate the graph 90°, then apply the vertical line test).
Generally, we don't describe these graphs as one-to-one, because we reserve that terminology for functions (as the textbook suggests). The terminology for a relation whose graph satisfies the horizontal line test but not the vertical line test is "injection", but this is not required knowledge for Methods.
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