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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![The expression in the image is:
\[ 6n^4 - 21n^2 - 12 \]
This is a polynomial expression of degree 4. It consists of three terms:
- The first term is \( 6n^4 \), where 6 is the coefficient and \( n \) is raised to the power of 4.
- The second term is \( -21n^2 \), where -21 is the coefficient and \( n \) is raised to the power of 2.
- The third term is -12, which is a constant term.
Polynomials of degree 4 are sometimes referred to as quartic polynomials. The degree of a polynomial is the highest power of the variable present in the polynomial, which for this expression is 4.
Polyynomials can be graphed, although the specific shape of the graph will depend on the coefficients of the terms. Typically, a quartic polynomial can have up to 3 turning points and 4 roots (including complex roots). In this particular polynomial, the negative term (\( -21n^2 \)) and the constant term (\( -12 \)) will influence the shape of the graph.
Visualization of such expressions is useful for understanding the behavior of the polynomial function, such as identifying the roots or the intervals where the function is increasing or decreasing.
On an educational website, this expression would typically be discussed in the context of polynomial functions, their properties, and their graphs.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd32c5a2f-ca13-423f-9b19-63c6eff85030%2Fc65e80ba-3972-49ea-ad9c-55976d70c589%2F9t6lwmc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The expression in the image is:
\[ 6n^4 - 21n^2 - 12 \]
This is a polynomial expression of degree 4. It consists of three terms:
- The first term is \( 6n^4 \), where 6 is the coefficient and \( n \) is raised to the power of 4.
- The second term is \( -21n^2 \), where -21 is the coefficient and \( n \) is raised to the power of 2.
- The third term is -12, which is a constant term.
Polynomials of degree 4 are sometimes referred to as quartic polynomials. The degree of a polynomial is the highest power of the variable present in the polynomial, which for this expression is 4.
Polyynomials can be graphed, although the specific shape of the graph will depend on the coefficients of the terms. Typically, a quartic polynomial can have up to 3 turning points and 4 roots (including complex roots). In this particular polynomial, the negative term (\( -21n^2 \)) and the constant term (\( -12 \)) will influence the shape of the graph.
Visualization of such expressions is useful for understanding the behavior of the polynomial function, such as identifying the roots or the intervals where the function is increasing or decreasing.
On an educational website, this expression would typically be discussed in the context of polynomial functions, their properties, and their graphs.
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