https://file.aiquickdraw.com/mathbot/file/1728914865671tzy7v69f.jpg

The question asks for the range of the function \( g(x) \), and the graph of \( g(x) \) is provided.

### Observations:
- As \( x \to -\infty \), the graph approaches but never reaches \( y = -3 \).
- As \( x \to 0^+ \) (from the right), the graph approaches \( y = +\infty \).
- The graph has a vertical asymptote at \( x = 0 \).
- As \( x \to 0^- \) (from the left), the graph approaches \( y = -4 \) but doesn't include \( y = -4 \) (as there's a hollow circle indicating an excluded value).
- The graph decreases as \( x \) becomes negative but doesn't reach below \( y = -3 \).

### Range:
- The function approaches all values from \( -\infty \) up to but not including \( y = -4 \), and from \( y = -3 \) upwards to \( \infty \), excluding \( y = -3 \) and \( y = -4 \).
  
Thus, the range of \( g(x) \) is:
\[
(-\infty, -4) \cup (-3, +\infty)
\]

This corresponds to option **A**: \( \{ y \in \mathbb{R} \, | \, y \neq -4, -3 \} \).

Would you like more details on how to interpret this? Here are 5 related questions:

1. What is the definition of a function's range?
2. How do vertical asymptotes affect the range of a function?
3. Why are certain values like \( y = -4 \) and \( y = -3 \) excluded from the range?
4. Can you explain how to find asymptotes from a graph?
5. What are some common types of discontinuities in functions?

**Tip:** When analyzing a graph, always check for asymptotes and points where the function is undefined to correctly determine the range.

What is the range of function g, as shown in the graph?

Learn how to determine the range of a function by analyzing its graph. This problem involves recognizing asymptotes and understanding how certain values are excluded from the function's range. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation