9. What value is the function approaching when the function is getting closer to x = 0? Explain

Algebra and Trigonometry (MindTap Course List)
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Author:James Stewart, Lothar Redlin, Saleem Watson
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Chapter3: Polynomial And Rational Functions
Section3.CT: Chapter Test
Problem 3CT: A cannonball fired out to sea from a shore battery follows a parabolic trajectory given by the graph...
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### Problem 9: Understanding the Behavior of a Function as x Approaches 0

**Question:**  
What value is the function approaching when the function is getting closer to \( x = 0 \)? Explain.

**Graph Explanation:**  
The image contains a plot of a parabolic function. The x-axis ranges from -4 to +4 and the y-axis ranges from -4 to +4. The graph is a symmetric parabola opening downwards, with its vertex at the point (0, 4).

**Detailed Analysis:**
- The function displayed in the graph is a downward-facing parabola.
- The vertex of the parabola, the highest point on the graph, lies at \( (0, 4) \).
- As \( x \) approaches 0 from either the positive or negative direction, the values of the function get closer to 4.
  
**Conclusion:**
When \( x \) gets closer to 0, the function is approaching the value 4. This conclusion is drawn by observing the vertex of the parabola, which represents the maximum value the function reaches.
Transcribed Image Text:### Problem 9: Understanding the Behavior of a Function as x Approaches 0 **Question:** What value is the function approaching when the function is getting closer to \( x = 0 \)? Explain. **Graph Explanation:** The image contains a plot of a parabolic function. The x-axis ranges from -4 to +4 and the y-axis ranges from -4 to +4. The graph is a symmetric parabola opening downwards, with its vertex at the point (0, 4). **Detailed Analysis:** - The function displayed in the graph is a downward-facing parabola. - The vertex of the parabola, the highest point on the graph, lies at \( (0, 4) \). - As \( x \) approaches 0 from either the positive or negative direction, the values of the function get closer to 4. **Conclusion:** When \( x \) gets closer to 0, the function is approaching the value 4. This conclusion is drawn by observing the vertex of the parabola, which represents the maximum value the function reaches.
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