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

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The function y = x^3 is confirmed to be one-to-one because it passes the horizontal line test. This test indicates that any horizontal line drawn will intersect the graph at most once. Therefore, each output value corresponds to exactly one input value. The graph's shape supports this conclusion, reinforcing its one-to-one nature. Thus, y = x^3 is indeed a one-to-one function.
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Is the function y = x^3 one-to-one? If not, why?
 
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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.
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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