- #1
In summary, The conversation discusses a problem where the function is only defined over a certain range, but the question asks to extend it beyond that range. The full problem statement is included and the issue with the period of the waveform is clarified. The use of Unicode and LaTeX characters is also mentioned as a way to improve the readability of mathematical expressions.
- #2
berkeman
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But your function looks to be only defined over -l to +l -- why are you asked to extend it outside of that definition? Is there more to the question? Is that really how the problem is stated in the book?
- #3
- #4
berkeman
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Ah, yes. You left out the "and" part...Setareh7796 said:
So the period of the waveform is 2l, right? So f(x) should equal f(2l), not f(3l/2)...
- #5
Mark44
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According to the belated problem statement, f(x) = f(x + 2l).berkeman said:
- #6
berkeman
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Yeah, thanks Mark. I meant f(x) = f(x + 2l), not = f(x + 3l/2). Trying to type too fast I guess...Mark44 said:
- #7
SammyS
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That " l ", lower case L, sure makes these expressions difficult to read. There is a Unicode character that will help, Unicode character U + 2113, which is rendered as ℓ .
f(x) = f(x + 2l) becomes f(x) = f(x + 2ℓ)
##\LaTeX##, can also give a good result. Its standard use of a serif font in italics for variables gives ##f(x) = f(x + 2l) ##.
But the script lowercase L can be displayed in ##\LaTeX##. Use "\ell" to get ##f(x) = f(x + 2\ell) ##.
Now I must say that "\ell" looks better written with ##\LaTeX## as \##ell##.
f(x) = f(x + 2l) becomes f(x) = f(x + 2ℓ)
##\LaTeX##, can also give a good result. Its standard use of a serif font in italics for variables gives ##f(x) = f(x + 2l) ##.
But the script lowercase L can be displayed in ##\LaTeX##. Use "\ell" to get ##f(x) = f(x + 2\ell) ##.
Now I must say that "\ell" looks better written with ##\LaTeX## as \##ell##.
FAQ: Sketching the graph of a function
What is the purpose of sketching the graph of a function?
Sketching the graph of a function allows us to visually understand and analyze the behavior of the function. It can help us identify important features such as zeros, extrema, and asymptotes.
What information do we need to sketch the graph of a function?
To sketch the graph of a function, we need to know the domain and range of the function, any critical points, and the behavior of the function at the endpoints of its domain.
How can we determine the shape of a function's graph?
The shape of a function's graph is determined by its degree and leading coefficient. For example, a linear function will have a straight line graph, while a quadratic function will have a parabolic graph.
Can we sketch the graph of any function?
While we can sketch the graph of most functions, there are some functions that cannot be easily sketched, such as those with infinitely many discontinuities or those with constantly changing behavior.
How can we use technology to help us sketch the graph of a function?
There are various graphing calculators and online tools that can help us sketch the graph of a function accurately and efficiently. These tools can also provide additional features such as zooming, tracing, and displaying the equation of the graph.