Maths-

General

Easy

Question

# Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.

Hint:

### A rational function is a function that is the ratio of polynomials. Any function of one variable, x, is called a rational function if, it can be represented as f(x) = p(x)/q(x), where p(x) and q(x) are polynomials such that q(x) ≠ 0.

Rational functions are of the form y = f(x)y = f x , where f(x)f x is a rational expression .

- If both the polynomials have the same degree, divide the coefficients of the leading terms. This is your asymptote.
- If the degree of the numerator is less than the denominator, then the asymptote is located at y = 0 (which is the x-axis).
- If the degree of the numerator is greater than the denominator, then there is no horizontal asymptote.

## The correct answer is: From the graph we can analyze that the vertical asymptote of the rational function is x= 6 and horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1/1=1

### 1.Find the asymptotes of the rational function, if any.

2.Draw the asymptotes as dotted lines.

3.Find the x -intercept (s) and y -intercept of the rational function, if any.

4.Find the values of y for several different values of x .

5.Plot the points and draw a smooth curve to connect the points. Make sure that the graph does not cross the vertical asymptotes.

The vertical asymptote of a rational function is x -value where the denominator of the function is zero. Equate the denominator to zero and find the value of x .

x - 6= 0

x = 6

The vertical asymptote of the rational function is x= 6

We will find more points on the function and graph the function.

From the graph we can analyze that the vertical asymptote of the rational function is x= 6 and horizontal asymptote is

y = (leading coefficient of numerator) / (leading coefficient of denominator) = =1

### Related Questions to study

Maths-

### Write an explicit formula for the arithmetic sequence.

### Write an explicit formula for the arithmetic sequence.

Maths-General

Maths-

### Write an explicit formula for the arithmetic sequence.

### Write an explicit formula for the arithmetic sequence.

Maths-General

Maths-

### Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.

### Use long Division to rewrite each rational function. Find the asymptotes of and sketch the graph.

Maths-General

Maths-

### The cost to rent a bike is 28 for the first day plus 2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?

### The cost to rent a bike is 28 for the first day plus 2 for each day after that. Write an explicit formula for the rental cost for n days. What is the cost of renting a bike for 8 days?

Maths-General

Maths-

### The daily attendance at an amusement park after day x is given by the function

f(x) =. On Approximately which day will the attendance be 1125 people ?

### The daily attendance at an amusement park after day x is given by the function

f(x) =. On Approximately which day will the attendance be 1125 people ?

Maths-General

Maths-

### Graph each function and identify the horizontal and vertical asymptotes

### Graph each function and identify the horizontal and vertical asymptotes

Maths-General

Maths-

### Graph each function and identify the horizontal and vertical asymptotes

### Graph each function and identify the horizontal and vertical asymptotes

Maths-General

Maths-

### Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3

### Write an equation of the line that passes through the point (4, 5) and is perpendicular to the graph of y = 2x + 3

Maths-General

Maths-

### Graph each function and identify the horizontal and vertical asymptotes

### Graph each function and identify the horizontal and vertical asymptotes

Maths-General

Maths-

### Graph each function and identify the horizontal and vertical asymptotes

### Graph each function and identify the horizontal and vertical asymptotes

Maths-General

Maths-

### Write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to .

### Write an equation of the line in slope-intercept form that passes through the point (-3, 5) and is parallel to .

Maths-General

Maths-

### What is the graph of f(x

### What is the graph of f(x

Maths-General

General

### Direction : Fill in the blank with correct letter.

J _ _ p

### Direction : Fill in the blank with correct letter.

J _ _ p

GeneralGeneral

English-One-to-One

### Direction : Identify the image and choose the correct word.

### Direction : Identify the image and choose the correct word.

English-One-to-OneGeneral

General

### Caroline loves reading history.

Which word is the gerund in the above sentence?

### Caroline loves reading history.

Which word is the gerund in the above sentence?

GeneralGeneral