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"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.
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What does the horizontal line tell you about a function?
If the function is a one-to-one function, therefore it has an inverse.
Is a piecewise function one to one?
A piecewise function can be one-to-one, but it is not guaranteed to be. A function is considered one-to-one if each element in the domain maps to a unique element in the range. In the case of a piecewise function, it depends on the specific segments and how they are defined. If each segment of the piecewise function passes the horizontal line test, then the function is one-to-one.
What is a type of function whose graph is a nonvertical line?
A monotonic, or one-to-one function.
Can an invertible function have more than one x-intercept?
No. If the function has more than one x-intercept then there are more than one values of x for which y = 0. This means that, for the inverse function, y = 0 should be mapped onto more than one x values. That is, the inverse function would be many-to-one. But a function cannot be many-to-one. So the "inverse" is not a function. And tat means the original function is not invertible.
What is one to one -function?
It is a surjection.
