# Difference between 1/x and Cosech (x) graph

• aurao2003
In summary, the conversation discusses the differences between the graphs of 1/x and Cosech(x). The experts suggest graphing the equations and comparing the table of values to see the differences. They also mention that the two graphs are not the same and have many differences. The person asking the question has already drawn the graphs, but is looking for a way to explain the differences to someone without a mathematical understanding.
aurao2003

## Homework Statement

Hi
Can anyone tell me the difference between the 1/x and Cosech(x) graph?
Thanks

## The Attempt at a Solution

You mean the hyperbolic cosecant?
$$g(x) = csch\;x = \frac{2}{e^x - e^{-x}}$$
Graph this and
$$f(x) = \frac{1}{x}$$
on your grapher and compare the table of values. Are they the same?

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?

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?
Yes! I have drawn them. But how would you explain the differences to someone without a mathematical understanding?

eumyang said:
You mean the hyperbolic cosecant?
$$g(x) = csch\;x = \frac{2}{e^x - e^{-x}}$$
Graph this and
$$f(x) = \frac{1}{x}$$
on your grapher and compare the table of values. Are they the same?
Thanks. My question is more in relation to a basic sketch and features.

## 1. What is the difference between 1/x and Cosech (x) graph?

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.

## 2. How do the graphs of 1/x and Cosech (x) differ?

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.

## 3. What is the domain and range of the 1/x and Cosech (x) functions?

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.

## 4. How do the asymptotes of 1/x and Cosech (x) differ?

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.

## 5. Which function is a better representation of a real-world phenomenon?

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.

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