How can an inequality be manipulated to show a specific range of values?

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The discussion focuses on how to manipulate the inequality -1 ≤ x ≤ 1 to demonstrate that 0 ≤ x² ≤ 1. The key point is that squaring any value of x within the range of -1 to 1 results in a non-negative value, hence the lower bound becomes 0. Additionally, since the maximum value of x in this range is 1, squaring it confirms that the upper bound remains 1. Visualizing the graph of x² over the interval clarifies this transformation. Understanding these properties of squaring helps in grasping the relationship between the two inequalities.
shawli
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In an example in my textbook, it says the following:

"If -1 ≤ x ≤ 1, then 0 ≤ x2 ≤ 1. "


Can someone explain to me how to move from the first statement to the second statement please? I'm not quite sure how the -1 turned into a 0...
 
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Did you draw a graph of x^2 on the interval -1 ≤ x ≤ 1?
 
Ah right... it's staring me right in the face! So clear that I missed it haha. Thank you!
 

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