The Vertical Line Test for Functions:
If any vertical line intercepts a graph in more than one point, the graph does not define y as a function of x.
By the definition of a function, for each value of x we can have at most one value for y.
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The Vertical Line Test for Functions: If any vertical line intercepts a graph in more than one point, the graph does not define y as a function of x. By the definition of a function, for each value of x we can have at most one value for y.
"y = f(x) is a function if it passes the vertical line test. It is a 1-1 function if it passes both the vertical line test and the horizontal line test. " - In order to be a one-to-one function, it first has to BE a function and pass the vertical line test. For example, a relation on a graph like a circle that does not pass the vertical line test is not function nor one-to-one.
A vertical test line is useful because, by definition, a function has one and only one result value for each input value. If you can find a vertical line that intersects the curve of the line, then it is not a function. A simple example is a circle.
Many to one function
Y = X2 ===== The graph of this parabola is crossed only at a point and once by a vertical line, so it is a function. Passes the vertical line test.