https://file.aiquickdraw.com/mathbot/file/173445748576806jfkux3.jpg

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.

What is the horizontal asymptote of the graph of \(f(x) = \frac{x+1}{x^2-3x-4}\)?

Discover how to find the horizontal asymptote of the rational function \(f(x) = \frac{x+1}{x^2-3x-4}\) with a detailed step-by-step solution. This problem explores key concepts in rational functions and polynomial degrees, making it ideal for students in Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation