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The graph of a polynomial of degree 5 is shown. State the number of real zeros and the number of imaginary zeros. 12 10 -8 6 2 C

The graph of a polynomial of degree 5 is shown. State the number of real zeros and the number of imaginary zeros. 12 10 -8 6 2 C

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
**Question:** 3. The graph of a polynomial of degree 5 is shown. State the number of real zeros and the number of imaginary zeros. **Graph Analysis:** The graph is a plot of a polynomial function of degree 5. It displays the behavior of the polynomial function across the x-y plane, intersecting the x-axis at certain points, which represent the real zeros. The y-values range from -16 to 12. **Key features of the graph:** 1. **Real Zeros:** The graph intersects the x-axis 3 times, indicating 3 real zeros. 2. **Turning Points:** There are several turning points visible, which is typical for a polynomial of this degree. 3. **Imaginary Zeros:** Since the polynomial is of degree 5 and there are 3 real zeros, there are 2 imaginary zeros (since the total number of zeros, including real and imaginary, must equal the degree of the polynomial, which is 5). The polynomial graph showcases a curving path characteristic of a quintic function, with various peaks and valleys.
Transcribed Image Text:**Question:** 3. The graph of a polynomial of degree 5 is shown. State the number of real zeros and the number of imaginary zeros. **Graph Analysis:** The graph is a plot of a polynomial function of degree 5. It displays the behavior of the polynomial function across the x-y plane, intersecting the x-axis at certain points, which represent the real zeros. The y-values range from -16 to 12. **Key features of the graph:** 1. **Real Zeros:** The graph intersects the x-axis 3 times, indicating 3 real zeros. 2. **Turning Points:** There are several turning points visible, which is typical for a polynomial of this degree. 3. **Imaginary Zeros:** Since the polynomial is of degree 5 and there are 3 real zeros, there are 2 imaginary zeros (since the total number of zeros, including real and imaginary, must equal the degree of the polynomial, which is 5). The polynomial graph showcases a curving path characteristic of a quintic function, with various peaks and valleys.
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