From the equation y= Negative 5X -20 over X squared -16 can you graph and tell me the vertical asymptote horizontal asymptote the x intercept and the y intercept and if wether or not it contains a hole

Here is the graph of the function \( y = \frac{-5x - 20}{x^2 - 16} \).

### Summary of Features:
1. **Vertical Asymptotes**: \( x = -4 \) and \( x = 4 \) (shown as red dashed lines).
2. **Horizontal Asymptote**: \( y = 0 \) (green dashed line).
3. **X-Intercept**: \( (-4, 0) \) (black point).
4. **Y-Intercept**: \( \left( 0, \frac{5}{4} \right) \) (purple point).
5. **No Holes** in the graph.

Let me know if you would like further details or have any questions!

Here are 5 related questions for deeper exploration:
1. How do you determine oblique asymptotes in rational functions?
2. How does factoring help in identifying holes in a graph?
3. What happens when the degree of the numerator is greater than the denominator?
4. Can you identify the behavior of the function as \( x \to \infty \)?
5. How do vertical asymptotes affect the domain of the function?

**Tip**: When finding vertical asymptotes, always check the factored form of both numerator and denominator for any common factors that could indicate a hole instead of an asymptote.

From the equation y = (-5x - 20) / (x^2 - 16), can you graph and tell me the vertical asymptote, horizontal asymptote, the x-intercept, the y-intercept, and whether or not it contains a hole?

This detailed analysis of the rational function y = (-5x - 20) / (x^2 - 16) covers key concepts such as vertical and horizontal asymptotes, intercepts, and the behavior of rational functions. Learn how to identify features like asymptotes and intercepts, and whether or not the function contains a hole. Suitable for Grades 10-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation