Maths-
General
Easy
Question
What are the vertical and horizontal asymptotes of the graph of each function?
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: From the graph we can analyze that the vertical asymptote of the rational function is x= -2 and x = 2. and horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator) = 1/3
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 .
3x2 -12= 0
3x2 = 12
x2 = 4
x = -2 or x = 2
The vertical asymptote of the rational function is x = −2 and x = 2
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= -2 and x = 2. and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) =
Related Questions to study
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
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
Maths-
What are the vertical and horizontal asymptotes of the graph of each function?
What are the vertical and horizontal asymptotes of the graph of each function?
Maths-General
Maths-
Are graphs of the equations parallel, perpendicular or neither?
Are graphs of the equations parallel, perpendicular or neither?
Maths-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
Maths-
Are graphs of the equations parallel, perpendicular or neither?
Are graphs of the equations parallel, perpendicular or neither?
Maths-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
Maths-
What are the horizontal asymptotes for the graph
What are the horizontal asymptotes for the graph
Maths-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
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
Maths-
Tell whether the given sequence is an arithmetic sequence. 1,-2,3,-4,5,...
Tell whether the given sequence is an arithmetic sequence. 1,-2,3,-4,5,...
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...
Tell whether the given sequence is an arithmetic sequence. 77,64,51,38,25,...
Maths-General
Maths-
Tell whether the given sequence is an arithmetic sequence. 1,15,29,43,57,....
Tell whether the given sequence is an arithmetic sequence. 1,15,29,43,57,....
Maths-General
Maths-
Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....
Write a recursive formula for the given sequence. 47, 39, 31, 23, 15, ....
Maths-General
Maths-
Write a recursive formula for the given sequence. 81,85,89,93,97,....
Write a recursive formula for the given sequence. 81,85,89,93,97,....
Maths-General
