Is the function y = x^3 one-to-one? If not, why?

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SUMMARY

The function y = x^3 is confirmed to be one-to-one based on its ability to pass the horizontal line test. This test determines if a function is one-to-one by checking if any horizontal line intersects the graph more than once. Since the graph of y = x^3 does not intersect any horizontal line more than once, it is definitively a one-to-one function.

PREREQUISITES
  • Understanding of the horizontal line test
  • Basic knowledge of function properties
  • Familiarity with graphing techniques
  • Concept of one-to-one functions
NEXT STEPS
  • Study the properties of one-to-one functions in detail
  • Learn about the horizontal line test and its applications
  • Explore other types of functions and their characteristics
  • Investigate inverse functions and their relationship with one-to-one functions
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Is the function y = x^3 one-to-one? If not, why?
 
Mathematics news on Phys.org
RTCNTC said:
Is the function y = x^3 one-to-one? If not, why?

sketch the graph ... if it passes the horizontal line test, it is 1-1.
 
Yes, it passes the horizontal line test and thus 1-1.
 

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