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Aug 8, 2012 · Dominance. When considering functions made up of the sums, differences, products or quotients of different sorts of functions (polynomials, exponentials and logarithms), or different powers of the same sort of function we say that one function dominates the other. This means that as x approaches infinity or negative infinity, the graph will ...
should dominate any power of . Therefore, the graph of this function should eventually aproach the the -axis as the function value approaches . If this function approaches , then it must get below and stay below , eventually. How far out in the domain do you need to go before this function eventually dips and stays below .
One set is said to dominate another if there is a function from the latter into the former. More formally, we have the following. Definition: Dominance. If A and B are sets, we say “ A dominates B ” and write | A |> | B | iff there is an injective function f with domain B and codomain A.
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In this video, we review the topic of end behavior of a function and illustrate some general strategies for determining the end behavior of a function. We co...
- 20 min
- 1962
- Andrew Misseldine
The question gives us two polynomial functions, 𝑓 of 𝑥 and 𝑔 of 𝑥. The question wants us to determine whether 𝑓 of 𝑥 or 𝑔 of 𝑥 is dominant by evaluating the limit as 𝑥 approaches ∞ of 𝑓 of 𝑥 divided by 𝑔 of 𝑥. First, let’s recall what it means for one function to dominate another function. For ...
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Domination is a highly informal term relating two functions. We say that one function dominates another if the magnitude of the ratio of the first function to the second increases without bound as the input increases without bound. More concisely, f (x) dominates g (x) if limx→∞g (x)f (x)=0. There is no common notation for this idea, but ...
