To solve for the horizontal asymptote of the given rational function:

$f(x) = \frac{x + 1}{x^2 - 3x - 4}$

Steps to Solve:

1. Degree of numerator: The numerator $x + 1$ is a polynomial of degree 1.
2. Degree of denominator: The denominator $x^2 - 3x - 4$ is a polynomial of degree 2.

Rule for Horizontal Asymptotes:

• When the degree of the denominator is greater than the degree of the numerator, the horizontal asymptote is: $y = 0$

Final Answer:

$y = 0$

Additional Questions for Practice:

1. What are the vertical asymptotes of the function $f(x) = \frac{x+1}{x^2 - 3x - 4}$?
2. How do you find the horizontal asymptote if the degrees of the numerator and denominator are equal?
3. What happens if the degree of the numerator is greater than the denominator in a rational function?
4. Factorize $x^2 - 3x - 4$ to find its roots.
5. Can a rational function have both horizontal and oblique asymptotes? Explain.

Tip:

For horizontal asymptotes:

• Compare the degrees of the numerator and denominator polynomials.