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 = fx , 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= --1/2 and horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator) = 6/2=3
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 .
2x + 1= 0
x = 
The vertical asymptote of the rational function is x =
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= and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = 
=3
Related Questions to study
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
General
Direction : Complete the following sentences by choosing suitable words:
The ____________ had a small birthday party celebration.
Direction : Complete the following sentences by choosing suitable words:
The ____________ had a small birthday party celebration.
GeneralGeneral
General
Direction : Identify the root word’s meaning in Greek or Latin for the following word:
Folio, Foliage
Direction : Identify the root word’s meaning in Greek or Latin for the following word:
Folio, Foliage
GeneralGeneral
General
Direction : Identify the root word’s meaning in Greek or Latin for the following word:
Autograph, Biography.
Direction : Identify the root word’s meaning in Greek or Latin for the following word:
Autograph, Biography.
GeneralGeneral
