To identify the horizontal asymptote of the function $f(x) = \frac{3}{5x}$, follow these steps:

1. Express the Function: $f(x) = \frac{3}{5x}$

2. Analyze the Behavior as $x$ Approaches Infinity:

   • As $x$ approaches infinity ($x \to \infty$), the term $\frac{3}{5x}$ becomes smaller and smaller, approaching zero.

3. Horizontal Asymptote:

   • Therefore, as $x$ approaches infinity or negative infinity, $f(x)$ approaches 0.

The horizontal asymptote of $f(x) = \frac{3}{5x}$ is $y = 0$.

Would you like more details or have any questions?

Here are some related questions:

1. What is the horizontal asymptote of $f(x) = \frac{2}{x}$?
2. How does the value of the numerator affect the horizontal asymptote in rational functions?
3. What happens to the horizontal asymptote if the denominator has a higher degree than the numerator?
4. Identify the vertical asymptote for $f(x) = \frac{3}{5x}$.
5. What is the horizontal asymptote for $f(x) = \frac{5x^2 + 3}{7x^2 - 2}$?
6. How do you find horizontal asymptotes for exponential functions?
7. Explain how to find the horizontal asymptote of $f(x) = \frac{3}{5x + 2}$.
8. Compare the horizontal asymptotes of $f(x) = \frac{3}{5x}$ and $g(x) = \frac{5x}{3}$.

Tip: Horizontal asymptotes show the behavior of a function as $x$ approaches infinity or negative infinity; they're key in understanding the long-term behavior of the function.