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384 336 288 240 192 144 96 48 -10-9-8--6 -5 -4 -3 -2 -1, -48 -96 -144 -92 -240 -288 -336 -384 1 2 3 4 5 6 7 8 9 10 x

384 336 288 240 192 144 96 48 -10-9-8--6 -5 -4 -3 -2 -1, -48 -96 -144 -92 -240 -288 -336 -384 1 2 3 4 5 6 7 8 9 10 x

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Title: Understanding the End Behavior of Polynomial Functions** The graph of \( y = f(x) \) is graphed below. What is the end behavior of \( f(x) \)? ![Graph] ### Graph Description The graph shows a smooth curve representing a polynomial function. The x-axis ranges from -10 to 10, and the y-axis ranges from -384 to 384. Key features of the graph include: - The curve starts in the third quadrant, rises and crosses into the second quadrant, dips down crossing the x-axis around \( x = -3 \). - It continues to rise, peaking in the first quadrant before falling again, crossing the x-axis around \( x = 7 \). - Finally, it descends back into the fourth quadrant. ### End Behavior Analysis Based on the graph, observe the following end behaviors: - As \( x \rightarrow -\infty \), the graph shows that \( y \rightarrow \infty \). - As \( x \rightarrow \infty \), the graph shows that \( y \rightarrow -\infty \). ### Answer Choices Select the correct end behavior: - \( \circ \) As \( x \rightarrow -\infty \), \( y \rightarrow \infty \) and as \( x \rightarrow \infty \), \( y \rightarrow -\infty \). - \( \circ \) As \( x \rightarrow -\infty \), \( y \rightarrow -\infty \) and as \( x \rightarrow \infty \), \( y \rightarrow \infty \). - \( \circ \) As \( x \rightarrow -\infty \), \( y \rightarrow \infty \) and as \( x \rightarrow \infty \), \( y \rightarrow \infty \). - \( \circ \) As \( x \rightarrow -\infty \), \( y \rightarrow -\infty \) and as \( x \rightarrow \infty \), \( y \rightarrow -\infty \). [Submit Answer] Understand the end behavior of polynomial functions to predict how they behave as the x-values become very large or very small. This knowledge is essential for understanding the long-term trends in various applications.
Transcribed Image Text:**Title: Understanding the End Behavior of Polynomial Functions** The graph of \( y = f(x) \) is graphed below. What is the end behavior of \( f(x) \)? ![Graph] ### Graph Description The graph shows a smooth curve representing a polynomial function. The x-axis ranges from -10 to 10, and the y-axis ranges from -384 to 384. Key features of the graph include: - The curve starts in the third quadrant, rises and crosses into the second quadrant, dips down crossing the x-axis around \( x = -3 \). - It continues to rise, peaking in the first quadrant before falling again, crossing the x-axis around \( x = 7 \). - Finally, it descends back into the fourth quadrant. ### End Behavior Analysis Based on the graph, observe the following end behaviors: - As \( x \rightarrow -\infty \), the graph shows that \( y \rightarrow \infty \). - As \( x \rightarrow \infty \), the graph shows that \( y \rightarrow -\infty \). ### Answer Choices Select the correct end behavior: - \( \circ \) As \( x \rightarrow -\infty \), \( y \rightarrow \infty \) and as \( x \rightarrow \infty \), \( y \rightarrow -\infty \). - \( \circ \) As \( x \rightarrow -\infty \), \( y \rightarrow -\infty \) and as \( x \rightarrow \infty \), \( y \rightarrow \infty \). - \( \circ \) As \( x \rightarrow -\infty \), \( y \rightarrow \infty \) and as \( x \rightarrow \infty \), \( y \rightarrow \infty \). - \( \circ \) As \( x \rightarrow -\infty \), \( y \rightarrow -\infty \) and as \( x \rightarrow \infty \), \( y \rightarrow -\infty \). [Submit Answer] Understand the end behavior of polynomial functions to predict how they behave as the x-values become very large or very small. This knowledge is essential for understanding the long-term trends in various applications.
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