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Math Forum - Ask Dr. Math Archives: Asymptotes
Rational Function: Given the rational function y=r(x)=(4x^6-x^4)/(x^5+5) describe its end behavior and find all vertical and horizontal asymptotes for r if
Asymptotes: Examples
That is, you will have either a horizontal asymptote or else a slant Since I have found a horizontal asymptote, I don't have to look for a slant
Asymptotes
If an asymptote is parallel with the x-axis, we call it a horizontal asymptote. A line y = b is a horizontal asymptote of a function f(x) <=> lim f(x)
3.6.htm
To find horizontal asymptotes we need to take the limit of the function as x approaches Find the horizontal asymptotes for the following functions:
Horizontal Asymptotes
If the degree (the largest exponent) of the numerator is less than the degree of the denominator, the horizontal asymptote is the x-axis (y = 0).


Asymptotes
If an asymptote is parallel with the x-axis, we call it a horizontal asymptote. A line y = b is a horizontal asymptote of a function f(x) <=> lim f(x)
3.6.htm
To find horizontal asymptotes we need to take the limit of the function as x approaches Find the horizontal asymptotes for the following functions:
Horizontal Asymptotes
If the degree (the largest exponent) of the numerator is less than the degree of the denominator, the horizontal asymptote is the x-axis (y = 0).
Horizontal_Asymptotes
Some rational functions have a horizontal asymptote, but not all. To find a horizontal asymptote, we recall that as x becomes very large in magnitude,
Visual Calculus - Horizontal Asymptotes
for a = 2 and b = 4 in blue. If L is the limit above, the red line is the graph of y = L + e and the green line is the graph of y = L - e.
Horizontal Asymptotes
which means that y = 0 .ie,x-axis is the horizontal asymptote. Let us consider another example for horizontal asymptotes
Math Forum - Ask Dr. Math
Namely, you believe that horizontal asymptotes cannot share points with the curve. A horizontal asymptote is a line or a curve that the curve approaches
Graphing Rational Functions
7) Use the vertical and horizontal asymptotes to help you sketch the graph. It must approach the vertical and horizontal asymptote.