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(-1,215, 2.113) (-2, 0) (1,0) (0, 0) (0.549, –0.631)

(-1,215, 2.113) (-2, 0) (1,0) (0, 0) (0.549, –0.631)

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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State the domain of the function.

State the range of the function.

Identify the end behavior of the function.

Identify the x – intercept(s). Write as ordered pairs.

Identify the y – intercept. Write as an ordered pair.

Identify the maximum of the function.

 

The graph presented is a detailed plot of a polynomial function. This graph is plotted on a Cartesian coordinate system, with the x-axis and y-axis clearly marked. Key features of the graph include: 1. **Zeroes of the Function:** - The curve intersects the x-axis at three points: \((-2, 0)\), \( (0, 0) \), and \( (1, 0) \). These points indicate the roots or zeroes of the polynomial, where the function's value is zero. 2. **Critical Points:** - A local maximum is identified near the coordinates \((-1.215, 2.113)\). This indicates a peak in the polynomial function, where the function changes from increasing to decreasing. - A local minimum occurs around \((0.549, -0.631)\), indicating the lowest point in this section of the curve where the function changes from decreasing to increasing. 3. **Shape of the Curve:** - The curve rises steeply from the bottom left, reaching its local maximum, then dips downward past the origin to the local minimum, and finally rises again sharply to the top right. This graph illustrates the behavior of polynomial functions, demonstrating key concepts such as roots, local maxima and minima, and the general curvature of the graph. It is an excellent tool for understanding the fundamental properties of polynomial equations in a visual format.
Transcribed Image Text:The graph presented is a detailed plot of a polynomial function. This graph is plotted on a Cartesian coordinate system, with the x-axis and y-axis clearly marked. Key features of the graph include: 1. **Zeroes of the Function:** - The curve intersects the x-axis at three points: \((-2, 0)\), \( (0, 0) \), and \( (1, 0) \). These points indicate the roots or zeroes of the polynomial, where the function's value is zero. 2. **Critical Points:** - A local maximum is identified near the coordinates \((-1.215, 2.113)\). This indicates a peak in the polynomial function, where the function changes from increasing to decreasing. - A local minimum occurs around \((0.549, -0.631)\), indicating the lowest point in this section of the curve where the function changes from decreasing to increasing. 3. **Shape of the Curve:** - The curve rises steeply from the bottom left, reaching its local maximum, then dips downward past the origin to the local minimum, and finally rises again sharply to the top right. This graph illustrates the behavior of polynomial functions, demonstrating key concepts such as roots, local maxima and minima, and the general curvature of the graph. It is an excellent tool for understanding the fundamental properties of polynomial equations in a visual format.
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