Maths-
General
Easy
Question
Use long division to rewrite each rational function, What are the asymptotes of f ? Sketch
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) = 
, 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)fx 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: x = -1 & x = 1, y = 0. 5
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 .
2x2 - 2= 0
2x2 = 2
x2 = 1
x = 1 or x = -1
The vertical asymptote of the rational function is x = 2We 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= -1 & x=1 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = 
=0.5
The vertical asymptote of the rational function is x = 2We 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= -1 & x=1 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) =
=0.5Related Questions to study
Maths-
Write an equation of a line that passes through the given line and is perpendicular to the given line.
Write an equation of a line that passes through the given line and is perpendicular to the given line.
Maths-General
Maths-
Write an equation of a line that passes through the given line and is parallel to the given line.
Write an equation of a line that passes through the given line and is parallel to the given line.
Maths-General
Maths-
Use long division to rewrite each rational function, What are the asymptotes of f ? Sketch the graph.
Use long division to rewrite each rational function, What are the asymptotes of f ? Sketch the graph.
Maths-General
Maths-
Write an equation of a line that passes through the given line and is parallel to the given line.
Write an equation of a line that passes through the given line and is parallel to the given line.
Maths-General
Maths-
A line passing through (6, a) and (9, -4) is parallel to 2x - 3y = 6. What is the value of a?
A line passing through (6, a) and (9, -4) is parallel to 2x - 3y = 6. What is the value of a?
Maths-General
Maths-
Gabriela is selling friendship bracelets for a school fundraiser. After the first day, she has 234 bracelets left. After the second day, she has 222 bracelets left. Assuming the sales pattern continues and it is an arithmetic sequence, how many bracelets will Gabriela have to sell after the fifth day?
Gabriela is selling friendship bracelets for a school fundraiser. After the first day, she has 234 bracelets left. After the second day, she has 222 bracelets left. Assuming the sales pattern continues and it is an arithmetic sequence, how many bracelets will Gabriela have to sell after the fifth day?
Maths-General
Maths-
Use long division to rewrite each rational function, What are the asymptotes of f? Sketch the graph.
Use long division to rewrite each rational function, What are the asymptotes of f? Sketch the graph.
Maths-General
Maths-
In a trail map, the equation 
represents the Tamiami Trail. Choose the equation for a perpendicular trail.
In a trail map, the equation represents the Tamiami Trail. Choose the equation for a perpendicular trail.
Maths-General
Maths-
After the first raffle drawing 497 tickets remain. After the second raffle drawing, 494 tickets remain. Assuming that the pattern continues, write an explicit formula for arithmetic sequence to represent the number of raffle tickets that remain after each drawing. How many tickets remain in the bag after the seventh raffle drawing?
After the first raffle drawing 497 tickets remain. After the second raffle drawing, 494 tickets remain. Assuming that the pattern continues, write an explicit formula for arithmetic sequence to represent the number of raffle tickets that remain after each drawing. How many tickets remain in the bag after the seventh raffle drawing?
Maths-General
Maths-
Use long division to rewrite each rational function, What are the asymptotes of f ? Sketch the graph.
Use long division to rewrite each rational function, What are the asymptotes of f ? Sketch the graph.
Maths-General
Maths-
In a trail map, the equation y = 
represents the Tamiami Trail. Choose the equation for a perpendicular trail.
In a trail map, the equation y = represents the Tamiami Trail. Choose the equation for a perpendicular trail.
Maths-General
Maths-
A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Graph the sequence for the first 5 rows.
A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Graph the sequence for the first 5 rows.
Maths-General
Maths-
Juanita is trying to determine the vertical and horizontal asymptotes for the graph of the function 
. Describe and correct the error Juanita made in determining the vertical and horizontal asymptotes.
Juanita is trying to determine the vertical and horizontal asymptotes for the graph of the function . Describe and correct the error Juanita made in determining the vertical and horizontal asymptotes.
Maths-General
Maths-
A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write an explicit formula to represent the number of chairs in the nth row.
A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write an explicit formula to represent the number of chairs in the nth row.
Maths-General
Maths-
A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write a recursive formula to represent the number of chairs in the nth row.
A city sets up 14 rows of chairs for an outdoor concert. Each row has 2 more rows than the row in front of it. Write a recursive formula to represent the number of chairs in the nth row.
Maths-General
