Find the horizontal asymptote, if any, of the graph of the rational function.

To find the horizontal asymptote of the rational function , we look at the degrees of the polynomial in the numerator and the denominator. Both the numerator and the denominator are of degree 2. When the degrees are the same, the horizontal asymptote is determined by the ratio of the leading coefficients.

Here, the leading coefficient of the numerator (20) and the leading coefficient of the denominator (5) gives us:

Thus, the horizontal asymptote of the function is .

Now, let’s dive a bit deeper! As approaches infinity, the higher degree terms dominate the behavior of the function, leading us to the asymptote. It’s a fascinating aspect of rational functions that shows how they simplify to their leading terms, much like how we tend to focus on the crucial details in any complex situation!

If you’re looking to further understand asymptotes, a great way to explore is through graphing tools. They let you visualize how the function behaves as it approaches the asymptote, offering a clear picture of this mathematical concept in action. Enjoy experimenting with graphs!