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YES!

Simply by taking a quick glance at a graph, you can see several characteristics of the function: local minimums/maximums, points of inflection, end behavior, asymptotes, etc etc...

If you wanted to find these without the graph, you would have to do some math which might end up being very time consuming for very complicated functions. Even worse: what if the function is not elementary, and you can't express it in terms of finite arithmetic operations?

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Find the amplitude and period of the functions and sketch their graphs y equals sin -x?

y = sin(-x)Amplitude = 1Period = 2 pi


What is vertical stretch and horizontal stretch?

They are transformations of plane graphs.


What are graphs that cannot represent functions?

Consider the graph of y= +/- sqrt(x). Notice that, for any value of x greater than 0, there are two values of this relation. To be a function a relation has to assign one value in the range to each value in the domain. So this cannot be a function, yet it has a perfectly ordinary graph.


Why is it important that you be able to use series like the Maclaurin to approximate the behavior of various functions?

Using series like the Maclaurin series to approximate functions is important because it simplifies complex calculations, making it easier to analyze and predict the behavior of functions near a certain point (usually around zero). This is especially useful in calculus and numerical methods, where exact solutions might be difficult or impossible to obtain. Additionally, these approximations can help in understanding properties such as continuity, differentiability, and integrability of functions. Overall, they serve as powerful tools in both theoretical and applied mathematics.


Is most difficult an adverb?

No, "most difficult" is not an adverb; it is a phrase that functions as an adjective. "Difficult" is the adjective, describing a noun, while "most" serves as a modifier indicating the highest degree of difficulty. In this context, "most difficult" is used to convey the idea of something being the hardest among various options.

Related Questions

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