Maths-
General
Easy

Question

What is the graph of the functionf left parenthesis x right parenthesis equals fraction numerator 2 x plus 1 over denominator 3 x minus 4 end fraction

hintHint:

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 fractionwhere 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: From the graph we can analyze that the vertical asymptote of the rational function is x= 4/3. and horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator) = 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 .
    3x - 4= 0
    3x = 4
    x = 4 over 3
    The vertical asymptote of the rational function is x=4 over 3
    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= 4 over 3. and horizontal asymptote is
    y = (leading coefficient of numerator) / (leading coefficient of denominator) = 2 over 3
     

    Related Questions to study

    General
    Maths-

    Write recursive formula and explicit formula. -15,-6,-3,12,21,...

    Write recursive formula and explicit formula. -15,-6,-3,12,21,...

    Maths-General
    General
    Maths-

    The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is perpendicular to the north path.

    The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is perpendicular to the north path.

    Maths-General
    General
    Maths-

    Write recursive formula and explicit formula. 62,57,52,47,42,...

    Write recursive formula and explicit formula. 62,57,52,47,42,...

    Maths-General
    parallel
    General
    Maths-

    Write recursive formula and explicit formula. -4, 5,14,23,32,...

    Write recursive formula and explicit formula. -4, 5,14,23,32,...

    Maths-General
    General
    Maths-

    What are the vertical and horizontal asymptotes of the graph of each function?
    fraction numerator x squared plus 5 x plus 4 over denominator 3 x squared minus 12 end fraction

    What are the vertical and horizontal asymptotes of the graph of each function?
    fraction numerator x squared plus 5 x plus 4 over denominator 3 x squared minus 12 end fraction

    Maths-General
    General
    Maths-

    The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.

    The equation 2x + 7 represents a north path on a map. Find the equation for a path that passes through the point (6, 3) and is parallel to the north path.

    Maths-General
    parallel
    General
    Maths-

    Write recursive formula and explicit formula. 12,19,26,33,40,...

    Write recursive formula and explicit formula. 12,19,26,33,40,...

    Maths-General
    General
    Maths-

    What are the vertical and horizontal asymptotes of the graph of each function?
    G left parenthesis x right parenthesis equals fraction numerator 2 x squared plus x minus 9 over denominator x squared minus 2 x minus 8 end fraction
     

    What are the vertical and horizontal asymptotes of the graph of each function?
    G left parenthesis x right parenthesis equals fraction numerator 2 x squared plus x minus 9 over denominator x squared minus 2 x minus 8 end fraction
     

    Maths-General
    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    y equals negative 5 x space straight & space 25 x plus 5 y equals 1

    Are graphs of the equations parallel, perpendicular or neither?
    y equals negative 5 x space straight & space 25 x plus 5 y equals 1

    Maths-General
    parallel
    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 93,86,79,72,66,...

    Tell whether the given sequence is an arithmetic sequence. 93,86,79,72,66,...

    Maths-General
    General
    Maths-

    Are graphs of the equations parallel, perpendicular or neither?
    y equals 2 x plus 6 space straight & space y equals 1 half x plus 3

    Are graphs of the equations parallel, perpendicular or neither?
    y equals 2 x plus 6 space straight & space y equals 1 half x plus 3

    Maths-General
    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 37,3,31,29,26,23,...

    Tell whether the given sequence is an arithmetic sequence. 37,3,31,29,26,23,...

    Maths-General
    parallel
    General
    Maths-

    What are the horizontal asymptotes for the graph
    f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction

    What are the horizontal asymptotes for the graph
    f left parenthesis x right parenthesis equals fraction numerator 3 x minus 2 over denominator x squared plus 7 x plus 12 end fraction

    Maths-General
    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...

    Tell whether the given sequence is an arithmetic sequence. 3,6,9,15,18,...

    Maths-General
    General
    Maths-

    Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...

    Tell whether the given sequence is an arithmetic sequence. 3,6,9,12,15,18,...

    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.