It looks like you've uploaded an image with a math problem about horizontal asymptotes of a rational function. To assist you, here's an explanation of how to find the horizontal asymptote for the given rational function:

The rational function is in the form:

$f(x) = \frac{ax^2 + bx + c}{dx^2 + ex + f}$

To determine the horizontal asymptote:

1. Compare the degrees of the numerator and denominator.
   • If the degree of the numerator (the highest power of $x$ in the numerator) is less than the degree of the denominator, the horizontal asymptote is at $y = 0$.
   • If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the leading coefficients (i.e., $y = \frac{a}{d}$, where $a$ and $d$ are the leading coefficients of the numerator and denominator).
   • If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote, but there may be an oblique asymptote.

Explanation of the filled-in statement:

Because the degree of the numerator is equal to or less than the degree of the denominator, the horizontal asymptote can be found from the ratio of the leading coefficients of the numerator and denominator.

Would you like me to go into more detail about finding horizontal asymptotes or any other related concepts? Let me know if you have further questions or need clarification.

Here are 5 related questions for further exploration:

1. How do you find vertical asymptotes in rational functions?
2. Can a rational function have both a vertical and horizontal asymptote?
3. What is the difference between horizontal and oblique asymptotes?
4. How do you determine the domain of a rational function?
5. How do you graph a rational function with asymptotes?

Tip: Always start by identifying the degrees of the numerator and denominator when analyzing asymptotes!