# Find equation of asymptotes: very basic

• 939
In summary: It's much better to write(5x^3 - 4x^2 + 11) / (2x (x^2 - 9))or, if you really want to make it clear, use LaTeX. (That's also the only way to write something like x2/3, which would be interpreted by most people as x2/3.)In summary, the conversation discusses finding the equations of asymptotes for a given function. The equation is written as y = (5x^3 - 4x^2 + 11) / (2x (x^2 - 9)), and it is clarified that the degree of the denominator is 3. The expert also gives
939

## Homework Statement

Find the equations of the asymptotes.

## Homework Equations

y = 5x^3 - 4x^2 + 11 / 2x (x^2 - 9)

( 5x^3 - 4x^2 + 11 is the numerator, 2x (x^2 - 9) is the denominator)

## The Attempt at a Solution

Vertical: x = 0, x = -3, x = 3
Horizontal: Quick question...

The degree of the numerator for the first coefficient of the numerator is 3, for first of the denominator it is 1, correct? Thus there is no horizontal asymptote?

OR

Is the degree of the denominator 3, because of 2x and then x^2, in which case it would be 5/2?

The second. The degree of the denominator is 3. 2x(x^2-9)=2x^3-18x.

Last edited:
You're getting slightly confused, but did arrive at the answer kinda. Basically for x large, the x^3 terms on both the denominator and numerator will dominate each expression. Since they are both of degree 3 (that is the highest power of x is 3 for each) we simply look at the coeffecients of both x^3 terms and this will give us the answer. The coeffecient on top is 5, and on the bottom is 2, hence we have an asymptote at y=5/2.

939 said:

## Homework Equations

y = 5x^3 - 4x^2 + 11 / 2x (x^2 - 9)

( 5x^3 - 4x^2 + 11 is the numerator, 2x (x^2 - 9) is the denominator)
I'm glad you clarified what you wrote. When you write fractions with multiple terms in either the numerator or denominator, put parentheses around the whole numerator or denominator.

Here is your equation as it should be written:
y = (5x^3 - 4x^2 + 11) / (2x (x^2 - 9))

Dick said:
The second. The degree of the denominator is 3. 2x(x^2-9)=2x^3-18x.

Gengar said:
You're getting slightly confused, but did arrive at the answer kinda. Basically for x large, the x^3 terms on both the denominator and numerator will dominate each expression. Since they are both of degree 3 (that is the highest power of x is 3 for each) we simply look at the coeffecients of both x^3 terms and this will give us the answer. The coeffecient on top is 5, and on the bottom is 2, hence we have an asymptote at y=5/2.
Thanks :).

Mark44 said:
I'm glad you clarified what you wrote. When you write fractions with multiple terms in either the numerator or denominator, put parentheses around the whole numerator or denominator.

Here is your equation as it should be written:
y = (5x^3 - 4x^2 + 11) / (2x (x^2 - 9))

Thanks, I learned something similar when using wolframalpha, but wasn't sure if I should always write them like that :).

When you write a fraction with inline text (as opposed to using LaTeX), you should always put parentheses around numerators and/or denominators that have multiple terms.
What you wrote -
5x^3 - 4x^2 + 11 / 2x (x^2 - 9)

would be interpreted by many as

5x3 - 4x2 + ##\frac{11}{2}## x(x2 - 9)

Pretty obviously, that's not what you intended.

## 1. What is an asymptote?

An asymptote is a line that a curve approaches but never touches. It can be horizontal, vertical, or oblique.

## 2. How do you find the equation of an asymptote?

To find the equation of an asymptote, set the denominator of the rational function equal to zero. Then, solve for the variable in the numerator. The resulting value is the y-intercept of the asymptote. The equation of the asymptote will be y = mx + b, where m is the slope and b is the y-intercept.

## 3. What is the difference between a horizontal and vertical asymptote?

A horizontal asymptote is a line that the curve approaches as the x-values become very large or very small. A vertical asymptote is a line that the curve approaches as the x-value approaches a certain value, but the function is undefined at that value.

## 4. Can a curve have more than one asymptote?

Yes, a curve can have multiple asymptotes. This can occur when the function has multiple vertical asymptotes or when it has an oblique asymptote in addition to a horizontal or vertical one.

## 5. How do asymptotes affect the graph of a function?

Asymptotes do not appear on the graph of a function, but they can help determine the behavior of the graph. They can indicate where the function is approaching infinity or where it is undefined. Asymptotes can also help identify the end behavior of the function.

• Calculus and Beyond Homework Help
Replies
6
Views
516
• Calculus and Beyond Homework Help
Replies
10
Views
742
• Calculus and Beyond Homework Help
Replies
9
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
1K
• Precalculus Mathematics Homework Help
Replies
5
Views
618
• Calculus and Beyond Homework Help
Replies
1
Views
610
• Calculus and Beyond Homework Help
Replies
4
Views
1K
• Calculus and Beyond Homework Help
Replies
7
Views
709
• Calculus and Beyond Homework Help
Replies
16
Views
2K
• Calculus and Beyond Homework Help
Replies
25
Views
744