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mathdad
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Is the function y = x^3 one-to-one? If not, why?
RTCNTC said:Is the function y = x^3 one-to-one? If not, why?
A function is considered one-to-one if each input (x-value) has a unique output (y-value). In other words, no two different inputs can have the same output. This is also referred to as a "one-to-one correspondence" or "injective" function.
No, the function y = x^3 is not one-to-one. This is because multiple inputs can result in the same output. For example, both x = 2 and x = -2 have an output of y = 8. This violates the definition of a one-to-one function.
The function y = x^3 is not one-to-one because it is an odd-degree polynomial function. This means that it has both positive and negative solutions, resulting in multiple inputs having the same output. In general, polynomial functions with an even degree (such as y = x^2) are not one-to-one.
No, a one-to-one function cannot have a horizontal line as its graph. This is because a horizontal line would have multiple inputs (x-values) with the same output (y-value), which violates the definition of a one-to-one function.
There are a few ways to determine if a function is one-to-one. One way is to use the horizontal line test, where you draw a horizontal line across the function's graph. If the line intersects the graph more than once, the function is not one-to-one. Another method is to check the function's algebraic representation for any potential for multiple inputs resulting in the same output, such as in the case of a polynomial function with an even degree.