# Finding Equation of Rational Function

• Veronica_Oles
In summary, the given problem is flawed as the point (-1.5, 0) is an x-intercept, not a y-intercept as stated. The equation must have (x-5) in both the numerator and denominator for the hole at x=5, an x in the denominator for the vertical asymptote at x=0, and a value of 2 in the numerator for the horizontal asymptote at g(x)=2. However, there is no indication of where the y-intercept would come into the equation.
Veronica_Oles

## Homework Statement

Must find equation meeting these requirements:
1. Hole at x=5
2. Vertical Asymptote at x= 0
3. Horiztonal Asymptote at g(x) = 2
4. Y-int at (-1.5, 0)

## The Attempt at a Solution

I know that there must be an (x-5) in both the numerator and denominator due to the hole in the graph. I know that there is an x in the denominator due to the vertical asymptote. And since the degree's have to be even (from top and bottom numerator and denominator) due to the the horizontal asymptote, there has to be a value of 2 in the numerator. Howevere now I am confused where the y-int comes into th equation?

Veronica_Oles said:

## Homework Statement

Must find equation meeting these requirements:
1. Hole at x=5
2. Vertical Asymptote at x= 0
3. Horiztonal Asymptote at g(x) = 2
4. Y-int at (-1.5, 0)
There is either an error in the problem you were given or you have copied it incorrectly. The point (-1.5, 0) is an x-intercept, not a y-intercept.
Veronica_Oles said:

## The Attempt at a Solution

I know that there must be an (x-5) in both the numerator and denominator due to the hole in the graph. I know that there is an x in the denominator due to the vertical asymptote. And since the degree's have to be even (from top and bottom numerator and denominator) due to the the horizontal asymptote, there has to be a value of 2 in the numerator. Howevere now I am confused where the y-int comes into th equation?

Mark44 said:
There is either an error in the problem you were given or you have copied it incorrectly. The point (-1.5, 0) is an x-intercept, not a y-intercept.
Okay that's good to know. The problem given was written like how I wrote it, meaning problem is flawed.

## 1. What is a rational function?

A rational function is a mathematical expression that can be written as a ratio of two polynomial functions. It is usually represented as f(x) = p(x)/q(x), where p(x) and q(x) are polynomial functions and q(x) is not equal to zero.

## 2. How do you find the equation of a rational function?

To find the equation of a rational function, you need to follow these steps:

• 1. Identify the numerator and denominator of the rational function.
• 2. Determine the degree of both the numerator and denominator.
• 3. Use the degree to determine the horizontal and vertical asymptotes.
• 4. Find the x- and y-intercepts by setting the numerator and denominator equal to zero.
• 5. Simplify the function if possible.
• 6. Write the final equation in the form f(x) = p(x)/q(x).

## 3. How do you determine the horizontal and vertical asymptotes of a rational function?

The horizontal asymptote of a rational function can be found by comparing the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

The vertical asymptote can be found by setting the denominator equal to zero and solving for x. The vertical asymptote is the value(s) of x that make the denominator zero.

## 4. How do you find the x- and y-intercepts of a rational function?

The x-intercept(s) can be found by setting the numerator equal to zero and solving for x. The y-intercept can be found by setting x = 0 and solving the function for y.

## 5. Can a rational function have more than one horizontal or vertical asymptote?

Yes, a rational function can have more than one horizontal and vertical asymptote. This depends on the degree and coefficients of the numerator and denominator of the function. For example, a rational function with a numerator of degree 2 and a denominator of degree 3 can have two horizontal asymptotes and three vertical asymptotes.

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