Maths-
General
Easy

Question

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.

hintHint:

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: x = -3 x = 4, y = 1 y = -4


    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 .

    x2 – x - 12= 0
    x2 – 4x + 3x - 12= 0
    x(x - 4) + 3(x - 4) = 0
    (x - 4)(x + 3)
    x = -3 and x = 4
    The vertical asymptote of the rational function is x= -3 and x= 4
    horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1 over 1=1
    Juanita has taken the horizontal asymptote as y = -4 is an error in her calculation.

    Related Questions to study

    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
    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
    General
    Maths-

    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

    Maths-General
    parallel
    General
    Maths-

    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?

    Maths-General
    General
    Maths-

    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

    Maths-General
    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    y equals 1 half semicolon space y equals negative 3

    Are graphs of the equations parallel, perpendicular or neither?
    y equals 1 half semicolon space y equals negative 3

    Maths-General
    parallel
    General
    Maths-

    What is the horizontal asymptote of the rational function
    straight F left parenthesis straight x right parenthesis equals fraction numerator a x squared plus b x plus c over denominator d x squared plus e x plus f end fraction

    What is the horizontal asymptote of the rational function
    straight F left parenthesis straight x right parenthesis equals fraction numerator a x squared plus b x plus c over denominator d x squared plus e x plus f end fraction

    Maths-General
    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    y = 2x + 1; 2x - y = 3

    Are graphs of the equations parallel, perpendicular or neither?
    y = 2x + 1; 2x - y = 3

    Maths-General
    General
    Maths-

    A Trainer mixed water with an electrolyte solution. Container is having 12 gal of 25%  electrolyte solution. The Concentration of electrolytes can be modelled byf left parenthesis x right parenthesis equals fraction numerator 4 over denominator x plus 12 end fraction  , Graph the function.

    A Trainer mixed water with an electrolyte solution. Container is having 12 gal of 25%  electrolyte solution. The Concentration of electrolytes can be modelled byf left parenthesis x right parenthesis equals fraction numerator 4 over denominator x plus 12 end fraction  , Graph the function.

    Maths-General
    parallel
    General
    Maths-

    Find the 12th term. -8, -5.5 , -3, -0.5, 2.0,....

    Find the 12th term. -8, -5.5 , -3, -0.5, 2.0,....

    Maths-General
    General
    Maths-

    Write an equation of a line that passes through the given line and is perpendicular to the given line.
    left parenthesis 4 comma 3 right parenthesis semicolon space 4 x minus 5 y equals 30

    Write an equation of a line that passes through the given line and is perpendicular to the given line.
    left parenthesis 4 comma 3 right parenthesis semicolon space 4 x minus 5 y equals 30

    Maths-General
    General
    Maths-

    Write recursive formula. -5,-8.5,-12,-15.5,-19,....

    Write recursive formula. -5,-8.5,-12,-15.5,-19,....

    Maths-General
    parallel
    General
    Maths-

    Write an equation of a line that passes through the given line and is perpendicular to the given line.
    left parenthesis negative 2 comma 5 right parenthesis semicolon space x equals 3

    Write an equation of a line that passes through the given line and is perpendicular to the given line.
    left parenthesis negative 2 comma 5 right parenthesis semicolon space x equals 3

    Maths-General
    General
    Maths-

    Find the vertical and horizontal asymptotes of rational function, then graph the function.
    straight F left parenthesis straight x right parenthesis equals fraction numerator x minus 1 over denominator 2 x plus 1 end fraction

    Find the vertical and horizontal asymptotes of rational function, then graph the function.
    straight F left parenthesis straight x right parenthesis equals fraction numerator x minus 1 over denominator 2 x plus 1 end fraction

    Maths-General
    General
    Maths-

    Write recursive formula. 2,6,10,14,18,....

    Write recursive formula. 2,6,10,14,18,....

    Maths-General
    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.