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What is the function and the limit?

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Anonymous

13y ago
Updated: 10/17/2024

A lot of people think of a function as an "equation," but it can be more general than that. In formal definitions, a function is a "rule" that assigns every input to exactly one output. You might see a function as a graph, an equation, a table, or an obnoxious person that shouts back at you every word you say, but in pig latin.

The limit of a function exists if, as the input x approaches something, the output f(x) approaches something--regardless of the output when x actually reaches the thing it approaches. The limit is the thing that f(x) approaches. For example, picture (or Google), the graph of f(x) = 1/x. As x approaches infinity (further and further to the right of the graph), the curve f(x) gets closer and closer to the x-axis--meaning it gets closer and closer to zero.

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13y ago

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