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Horizontal asymptote is used to determine the range of a function just in case of a rational function. For example, the HA of f (x) = (2x) / (x 2 +1) is y = 0 and its range is {y ∈ R | y ≠ 0}. The horizontal asymptote is a horizontal line to which the graph of the function is very close to.
- Overview
- What is a horizontal asymptote?
- How do I find a horizontal asymptote of a rational function?
- Horizontal Asymptote Rules and Results
- Are horizontal asymptotes the same as slant asymptotes?
1 What is a horizontal asymptote?
2 How do I find a horizontal asymptote of a rational function?
If you see a dashed or dotted horizontal line on a graph, it refers to a horizontal asymptote (HA). In a rational function, an equation with a ratio of 2 polynomials, an asymptote is a line that curves closely toward the HA. The HA helps you see the end behavior of a rational function. In this article, we'll show you how to find the horizontal asymptote and interpret the results of your findings.
A horizontal asymptote is the dashed horizontal line on a graph. The graphed line of the function can approach or even cross the horizontal asymptote.
To find a horizontal asymptote, compare the degrees of the polynomials in the numerator and denominator of the rational function.
The degree of difference between the polynomials reveals where the horizontal asymptote sits on a graph.
A horizontal asymptote (HA) is a line that shows the end behavior of a rational function.
When you look at a graph, the HA is the horizontal dashed or dotted line. When you plot the function, the graphed line might approach or cross the HA if it becomes infinitely large or infinitely small.
Remove all terms but the terms with the biggest exponents of .
Since you're not actually solving an equation, you're simply comparing the leading terms in your rational function.
For example, if your equation is
, remove all but the leading terms to get
As another example, your equation might be
After you remove all but the leading terms, you'll have
If the degree of the numerator and denominator is the same, use the coefficient ratio.
If the polynomials in the numerator and denominator cancel each other out, you're left with the coefficients. Use the ratio of the coefficients to find the HA.
Going back to our first example of
, you ended up with
In this example, the HA is
If the numerator is at a lower degree, then the HA is located at y=0.
Horizontal asymptotes can be slanted if the degree of the numerator is greater by 1.
, perform polynomial long division. Note that as you find the slant asymptote, you'll also
This article was reviewed by
and by wikiHow staff writer,
Horizontal asymptote. A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches ±∞. It is not part of the graph of the function. Rather, it helps describe the behavior of a function as x gets very small or large.
20 de dic. de 2023 · Horizontal asymptotes, or HA, are horizontal dashed lines on a graph that help determine the end behavior of a function. They show how the input influences the graph’s curve as it extends toward infinity. Mathematically, they can be represented as the equation of a line y = b when either lim x → ∞ = b or lim x → − ∞ = b.
What is a horizontal asymptote? A horizontal asymptote for a rational function is a horizontal line, derived from the rational function, that shows you where the graph is, or thereabouts, when the graph goes off to the sides. MathHelp.com. How does a horizontal asymptote differ from a vertical asymptote?
Gráficas de funciones racionales: asíntota horizontal. Sal escoge la gráfica que corresponde a f (x)= (-x²+ax+b)/ (x²+cx+d), de acuerdo a su asíntota horizontal.
We know that a horizontal asymptote as x approaches positive or negative infinity is at negative one, y equals negative one. Here, our horizontal asymptote is at y is equal to zero. The graph approaches, it approaches the x axis from either above or below.
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