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# What does a horizontal asymptote represent?

Last updated date: 20th Mar 2023
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Hint: There are three different types of asymptotes: horizontal, vertical and oblique. In this question, we are going to discuss horizontal asymptotes. Generally, a horizontal asymptote is a horizontal line that represents the behavior of a function when the value of $x$ is extremely small or large.

Horizontal Asymptote: Horizontal asymptote of a given function represents the values of $f\left( x \right)$ , when $x$ is significantly small or large.
Generally, the equations of horizontal asymptote are represented by $y = a$ , where $a$ is the value of $y$ when $x \to \pm \infty$ .
We can find the horizontal asymptote of a function by determining the function’s restricted output values. Horizontal asymptote is simply the value of $\mathop {\lim }\limits_{x \to \infty } f\left( x \right)$ .
In the above graph, $f\left( x \right) = \dfrac{{4{x^3}}}{{{x^2}}}$ and line $y = 0.5$ shows us the horizontal asymptote and the line $x = 0.7$ shows the vertical asymptote.