what are the vertical asymptotes of y=3x2/x2-25?

To find the vertical asymptotes of the function:

\[
y = \frac{3x^2}{x^2 - 25}
\]

we look for the values of \( x \) that make the denominator zero, because a vertical asymptote occurs where the function tends to infinity due to division by zero.

### Step 1: Set the denominator equal to zero.

\[
x^2 - 25 = 0
\]

### Step 2: Solve for \( x \).

\[
x^2 = 25
\]
\[
x = \pm 5
\]

### Conclusion:
The vertical asymptotes occur at \( x = 5 \) and \( x = -5 \).

Would you like more details on vertical asymptotes, or do you have any questions?

---

Here are 5 related questions:
1. How can you find horizontal asymptotes of the same function?
2. What is the domain of this function?
3. How do you graph a rational function with asymptotes?
4. How do you determine slant (oblique) asymptotes?
5. What happens to the graph near the vertical asymptotes?

**Tip:** When solving rational functions, always check both the numerator and the denominator for simplifications before finding asymptotes!

Discover how to find the vertical asymptotes of the rational function y = 3x^2 / (x^2 - 25). This step-by-step guide explains the process of solving x^2 - 25 = 0, identifying vertical asymptotes at x = 5 and x = -5. Ideal for high school students (Grades 9-12) learning about rational functions and asymptotes.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation