3. Which of the following statements are true given the graph below? I. The polynomial has an equal number of relative minimum(s) and maximum(s) II. As x- III. As x o , f(x) - ,f(x) -0- 00 1. I and II 2. Il and III 3. I and III 4. 1, 11, and II

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Transcription for Educational Website:**

**Question 3:**

Which of the following statements are true given the graph below?

I. The polynomial has an equal number of relative minimum(s) and maximum(s)  
II. As \( x \to -\infty \), \( f(x) \to -\infty \)  
III. As \( x \to \infty \), \( f(x) \to \infty \)  

![Graph with axes and polynomial curve]

Options:  
1. I and II  
2. II and III  
3. I and III  
4. I, II, and III  

**Graph Explanation:**

The graph depicts a polynomial curve with a distinct pattern of turning points. It shows one relative maximum and one relative minimum. The curve moves downwards as \( x \) approaches negative infinity, indicating that the function \( f(x) \) trends towards negative infinity. Conversely, as \( x \) approaches positive infinity, the function \( f(x) \) trends towards positive infinity.
Transcribed Image Text:**Transcription for Educational Website:** **Question 3:** Which of the following statements are true given the graph below? I. The polynomial has an equal number of relative minimum(s) and maximum(s) II. As \( x \to -\infty \), \( f(x) \to -\infty \) III. As \( x \to \infty \), \( f(x) \to \infty \) ![Graph with axes and polynomial curve] Options: 1. I and II 2. II and III 3. I and III 4. I, II, and III **Graph Explanation:** The graph depicts a polynomial curve with a distinct pattern of turning points. It shows one relative maximum and one relative minimum. The curve moves downwards as \( x \) approaches negative infinity, indicating that the function \( f(x) \) trends towards negative infinity. Conversely, as \( x \) approaches positive infinity, the function \( f(x) \) trends towards positive infinity.
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