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How many times can a horizontal line intersect the graph of a function that is one to one?

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Final answer:

A horizontal line intersects the graph of a one-to-one function at exactly one point, as multiple intersections would violate the function's one-to-one property.

Step-by-step explanation:

A horizontal line can intersect the graph of a function that is one-to-one only once. A function is called one-to-one if each y-value corresponds to exactly one x-value. Since a horizontal line has the same y-value across its length, if a one-to-one function intersects it more than once, that would mean there are multiple x-values for the same y-value, which violates the definition of a one-to-one function. Therefore, the intersection of a horizontal line and a one-to-one function's graph is always exactly one point.

A horizontal line can intersect the graph of a one-to-one function a maximum of one time.

A one-to-one function has the property that for every input value (x), there is a unique output value (y). Since a horizontal line has a constant y-value, it can intersect a one-to-one function at most once. This is because if the line intersects the function at two or more points, it would mean that there are multiple values of x that produce the same y-value, which violates the definition of a one-to-one function.

For example, consider the function y = x. If we draw a horizontal line at y = 2, it will intersect the graph of the function at a single point (2, 2).

User Thomas Jager
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