Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Use long division to rewrite each rational function, What are the asymptotes of f ? Sketch the graph.
$F left parenthesis x right parenthesis equals fraction numerator 6 x squared over denominator 1 plus 3 x squared end fraction$

hint 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) = $fraction numerator straight p left parenthesis straight x right parenthesis over denominator straight q left parenthesis straight x right parenthesis end fraction$ , 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: As square cannot be negative the given function has no asymptote

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 .
1 + 3x²= 0
x² = $fraction numerator negative 1 over denominator 3 end fraction$
As square cannot be negative the given function has no asymptote

Related Questions to study

Write an equation of a line that passes through the given line and is parallel to the given line.
$left parenthesis 2 comma 1 right parenthesis semicolon space y equals negative 3 x plus 8$

Write an equation of a line that passes through the given line and is parallel to the given line.
$left parenthesis 2 comma 1 right parenthesis semicolon space y equals negative 3 x plus 8$

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?

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?

parallel

Use long division to rewrite each rational function, What are the asymptotes of f? Sketch the graph.
$straight F left parenthesis straight x right parenthesis equals fraction numerator 5 x over denominator x minus 2 end fraction$

Use long division to rewrite each rational function, What are the asymptotes of f? Sketch the graph.
$straight F left parenthesis straight x right parenthesis equals fraction numerator 5 x over denominator x minus 2 end fraction$

In a trail map, the equation $y equals 1 half x plus 1$ represents the Tamiami Trail. Choose the equation for a perpendicular trail.
$y equals negative 2 x plus 4$

In a trail map, the equation $y equals 1 half x plus 1$ represents the Tamiami Trail. Choose the equation for a perpendicular trail.
$y equals negative 2 x plus 4$

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?

parallel

Use long division to rewrite each rational function, What are the asymptotes of f ? Sketch the graph.
$F left parenthesis x right parenthesis equals fraction numerator 2 x over denominator x plus 4 end fraction$

Use long division to rewrite each rational function, What are the asymptotes of f ? Sketch the graph.
$F left parenthesis x right parenthesis equals fraction numerator 2 x over denominator x plus 4 end fraction$

In a trail map, the equation y = $1 half x space plus space 1$ represents the Tamiami Trail. Choose the equation for a perpendicular trail.
$y equals 1 half x plus 5$

In a trail map, the equation y = $1 half x space plus space 1$ represents the Tamiami Trail. Choose the equation for a perpendicular trail.
$y equals 1 half x plus 5$

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.

parallel

Juanita is trying to determine the vertical and horizontal asymptotes for the graph of the function $f left parenthesis x right parenthesis equals fraction numerator x squared plus 3 x minus 4 over denominator x squared minus x minus 12 end fraction$ . 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 $f left parenthesis x right parenthesis equals fraction numerator x squared plus 3 x minus 4 over denominator x squared minus x minus 12 end fraction$ . Describe and correct the error Juanita made in determining the vertical and horizontal asymptotes.

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 n^th 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 n^th 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 n^th 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 n^th row.

parallel

Are graphs of the equations parallel, perpendicular or neither?
$negative 2 x plus 5 y equals negative 4 semicolon space y equals negative 5 over 2 x plus 6$

Are graphs of the equations parallel, perpendicular or neither?
$negative 2 x plus 5 y equals negative 4 semicolon space y equals negative 5 over 2 x plus 6$

Casey opened a saving account with a $$$ 50 deposit. For every month after the first month she deposits $$$ 25. Write an explicit rule to represent the amount of money being deposited in her account. How much money will Casey have in her account after 24 months?

Casey opened a saving account with a $$$ 50 deposit. For every month after the first month she deposits $$$ 25. Write an explicit rule to represent the amount of money being deposited in her account. How much money will Casey have in her account after 24 months?

Are graphs of the equations parallel, perpendicular or neither?
$x equals 4 semicolon space y equals 4$

Are graphs of the equations parallel, perpendicular or neither?
$x equals 4 semicolon space y equals 4$

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.