One to one function and y=x
Algebra
Level
2
Is it true that a graph of y=f(x) must always intersect the line y=x at least once?
No
Yes
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1 solution
No. For example, any function of the form f ( x ) = x + C for C ∈ R will have no fixed points (i.e. points ( x , f ( x ) ) with x = f ( x ) ). This alone provides an uncountably infinite yet by no means complete set of counterexamples.