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The validity or invalidity of a function are not abstract but depend on its domain and codomain or range.
If for any point, A, in the domain there is a unique point, B, in the range such that f(A) = B then the function is valid at A.
The validity of a function can change from point to point.
For example, f(x) = sqrt(x) is not a function from the set of Real Numbers to the set of Real Numbers because any negative number in the domain is not mapped to any value in the range. This can be corrected either by changing the domain to the set of non-negative Real Numbers or (if you are a more advanced mathematician) change the range to the set of Complex Numbers.
Similarly the reciprocal function, f(x) = 1/x is valid everywhere except for x = 0.
Or f(x) = tan(x) is valid except for x = 90+k*180 degrees for all integer values of k - so it is not valid at an infinite number of points.
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What does a one to one function look like?
One to one functions on a graph can vary. To determine if a function is one to one, a horizontal line can only intersect the function once. If it intersects the function more than once, it is not a one to one function.
How can one determine the median from a graph?
The answer depends on what the graph is of: the distribution function or the cumulative distribution function.
What is the horizantal line test and vertical line test?
Horizonatal line test is a test use to determine if a function is one-to-one. If a horizontal line intersects a function's graph more than once, then the function is not one-to-one. A one-to-one function is a function where every element of the range correspons to exactly one element of the domain. Vertical line test is a test used to determine if a function is a function or relation. If you can put a vertical line through graph and it only hits the graph once, then it is a function. If it hits more than once, then it is a relation.
How do you determine whether a graph of a mathematical relationship is a function?
If a vertical line, within the domain of the function, intersects the graph in more than one points, it is not a function.
What is The test to determine if a graph is a function is?
A graph is represents a function if for every value x, there is at most one value of y = f(x).
