Question
Identify the vertical and horizontal asymptotes of each rational function.
The correct answer is: From the graph we can analyze that the vertical asymptote of the rational function is x= -1/2 & x=1/2 and horizontal asymptote is y = (leading coefficient of numerator) / (leading coefficient of denominator) = 3/4
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.
Solution:-
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 .
4x2 - 1= 0
4x2 = 1
x2 = 
x=
or x = 
The vertical asymptote of the rational function is x= or 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= & x = and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) =
Related Questions to study
The graphs of
and 
are parallel lines. What is the value of ?
When two lines have distinct y-intercepts but the same slope, they are said to be parallel. They are perpendicular if the slopes of two lines are negative reciprocals of one another.
Parallel-Line: Two or more lines present in the same plane but never crossing each other are said to be parallel lines. They don't have anything in common.
Perpendicular-Line: Perpendicular lines are two lines that meet at an intersection point, which form 4 right angles.
Slope: The slope of a line indicates how sharp it is and is calculated by dividing the distance that a point on the line must travel horizontally and vertically to reach another point. Y-Intercept: Y-Intercept is the point at which the graph crosses the y-axis. From the Given Equation, the parallel lines can be written as 3x-9y=15 and y=mx-4. If the corresponding angles are equal, the two lines are considered parallel.
The graphs of and are parallel lines. What is the value of ?
When two lines have distinct y-intercepts but the same slope, they are said to be parallel. They are perpendicular if the slopes of two lines are negative reciprocals of one another.
Parallel-Line: Two or more lines present in the same plane but never crossing each other are said to be parallel lines. They don't have anything in common.
Perpendicular-Line: Perpendicular lines are two lines that meet at an intersection point, which form 4 right angles.
Slope: The slope of a line indicates how sharp it is and is calculated by dividing the distance that a point on the line must travel horizontally and vertically to reach another point. Y-Intercept: Y-Intercept is the point at which the graph crosses the y-axis. From the Given Equation, the parallel lines can be written as 3x-9y=15 and y=mx-4. If the corresponding angles are equal, the two lines are considered parallel.
represents the Tamiami Trail. Choose the equation for a perpendicular trail.
