https://file.aiquickdraw.com/mathbot/file/1729346332375m3bjlfp3.jpg

The graph in the image shows a rational function with a vertical asymptote at \(x = 3\) and a horizontal asymptote at \(y = 0\). Based on the shape of the graph, it appears that the function approaches negative infinity as \(x\) approaches 3 from the left, and approaches positive infinity as \(x\) approaches 3 from the right. The function does not cross the horizontal asymptote \(y = 0\), meaning the range does not include 0.

### Range of the function:
The function seems to take on all real values except \(y = 0\). Therefore, the range is:
\[
(-\infty, 0) \cup (0, \infty)
\]

Would you like further details on the reasoning, or have any questions?

---

Here are 5 related questions to expand on this:

1. What is the domain of this function?
2. How do vertical and horizontal asymptotes affect the range and domain of a function?
3. What is a rational function and how can its graph be analyzed?
4. How would the function behave if the asymptote were at a different value, such as \(y = 2\)?
5. How do you find the range of more complex functions?

**Tip**: When determining the range of a rational function, always pay attention to horizontal asymptotes and any restrictions where the function is undefined.

What is the range of the function shown in the graph below?

Understand how to find the range of a rational function by analyzing its vertical and horizontal asymptotes. This example includes a graph with a vertical asymptote at x=3 and a horizontal asymptote at y=0, illustrating the function's behavior as it approaches these 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