Question
Identify the vertical and horizontal asymptotes of each rational 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: x = 1 & x =-1, y = 5/2
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 .
2x2 - 2= 0
x2 = 1
x = 1 or x = -1
The vertical asymptote of the rational function is x = 1 or -1 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= 1 & x=-1 and horizontal asymptote is
y = (leading coefficient of numerator) / (leading coefficient of denominator) = 
Related Questions to study
Graph the function
Graph the function
Identify the vertical and horizontal asymptotes of each rational function.
Identify the vertical and horizontal asymptotes of each rational function.
Identify the vertical and horizontal asymptotes of each rational function.
Identify the vertical and horizontal asymptotes of each rational function.
Identify the vertical and horizontal asymptotes of each rational function.
Identify the vertical and horizontal asymptotes of each rational function.
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.
