- #1
aurao2003
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Homework Statement
Hi
Can anyone tell me the difference between the 1/x and Cosech(x) graph?
Thanks
Yes! I have drawn them. But how would you explain the differences to someone without a mathematical understanding?HallsofIvy said:That's a very strange question! The two graphs are not at all the same! There are so many differences, what kind of answer are you looking for? HAVE you actually draw the graphs yourself?
Thanks. My question is more in relation to a basic sketch and features.eumyang said:You mean the hyperbolic cosecant?
[tex]g(x) = csch\;x = \frac{2}{e^x - e^{-x}}[/tex]
Graph this and
[tex]f(x) = \frac{1}{x}[/tex]
on your grapher and compare the table of values. Are they the same?
1/x and Cosech (x) are two different mathematical functions that represent different types of graphs. The 1/x function represents a hyperbola, while the Cosech (x) function represents a hyperbolic cosecant curve.
The main difference between the 1/x and Cosech (x) graphs is their shape. The 1/x graph is a hyperbola that has two branches, while the Cosech (x) graph is a symmetric curve that approaches the x-axis but never touches it.
The domain of both functions is all real numbers except for x = 0. However, the range of the 1/x function is all real numbers except for y = 0, while the range of the Cosech (x) function is all real numbers except for y = ±1.
The 1/x graph has two asymptotes, one at x = 0 and the other at y = 0. The Cosech (x) graph has two asymptotes as well, one at x = 0 and the other at y = ±1.
It depends on the specific phenomenon being represented. The 1/x function is commonly used to model inverse relationships, while the Cosech (x) function is often used in physics to represent the motion of a damped harmonic oscillator.