https://file.aiquickdraw.com/mathbot/file/17292141146121gukjqur.jpg

The graph provided shows a rational function with vertical asymptotes, which are the vertical lines where the function tends toward infinity or negative infinity. Vertical asymptotes occur when the denominator of the rational function equals zero and the numerator is non-zero.

From the graph, the function seems to have vertical asymptotes at the following values of \( x \):
- \( x = -2 \)
- \( x = 1 \)

These are the points where the function's graph shoots up or down without crossing those lines.

### The vertical asymptotes of the function are:
\[
x = -2, 1
\]

Would you like further details on how vertical asymptotes are determined for rational functions, or any other related concepts?

---

Here are 5 questions to expand your understanding:
1. How do you determine vertical asymptotes from the equation of a rational function?
2. What happens to the function's value as it approaches a vertical asymptote?
3. Can rational functions have both vertical and horizontal asymptotes?
4. How are vertical asymptotes related to the denominator of a rational function?
5. How do you distinguish vertical asymptotes from holes in a graph?

**Tip**: To find vertical asymptotes in rational functions, focus on the values of \(x\) that make the denominator zero but not the numerator.

Determine the vertical asymptotes of the function f from the given graph. If there are multiple, enter your answer as a comma-separated list.

Learn how to identify vertical asymptotes from the graph of a rational function. This problem focuses on recognizing the points where the function approaches infinity or negative infinity. Suitable for students in Grades 10-12 studying algebra and rational functions.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation