Kinney’s use of the number line as a visual heuristic effectively demystifies the logical branching inherent in piecewise functions. It is a precise pedagogical exercise that replaces rote memorization with spatial intuition.
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PIECEWISE Functions: Use CASES with INEQUALITIES in MATHAñadido:
And with a peace-wise function like this, you've got cases. And for the given input -1/3, in this case, you've got to decide which case is it in. Inequalities sometimes confuse people. You got to be careful! It's the second case: -1/3 is greater than -1. On a number line, - 1/3 is to the right of -1 is therefore greater than -1. So it fits the second case.
So you use the second formula. You replace x with the input -1/3 and you get -1 + 1 is zero.
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