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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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How many negative real zeroes does the function f have?
The image shows a graph of a mathematical function plotted on a Cartesian coordinate system. Here's a detailed description of the graph: - **Axes**: The graph features two axes; the horizontal axis (x-axis) labeled as "x" and the vertical axis (y-axis) labeled as "y". Both axes contain tick marks with numerical values. The x-axis ranges approximately from -6 to 6, and the y-axis ranges approximately from -15 to 15. - **Curve**: The curve is a continuous smooth blue line representing the function. The shape suggests it is a polynomial with multiple turning points: - It starts in the top-left, descending to a local minimum. - It then ascends to a local maximum before descending again to a global minimum. - Finally, it ascends sharply towards the top-right. - **Intersections**: The curve crosses the x-axis (roots of the equation) at two points, indicating there are real roots. - **Central Feature**: The plot appears to be symmetric vertically about the point where it reaches its global minimum on the y-axis. - **Button**: Below the graph, there is an "OK" button, which suggests that the image might be from a software application or an online tool used for graphing or educational purposes. This graph can help students understand concepts like polynomial roots, turning points, and the behavior of quadratic or higher-degree polynomials.
Transcribed Image Text:The image shows a graph of a mathematical function plotted on a Cartesian coordinate system. Here's a detailed description of the graph: - **Axes**: The graph features two axes; the horizontal axis (x-axis) labeled as "x" and the vertical axis (y-axis) labeled as "y". Both axes contain tick marks with numerical values. The x-axis ranges approximately from -6 to 6, and the y-axis ranges approximately from -15 to 15. - **Curve**: The curve is a continuous smooth blue line representing the function. The shape suggests it is a polynomial with multiple turning points: - It starts in the top-left, descending to a local minimum. - It then ascends to a local maximum before descending again to a global minimum. - Finally, it ascends sharply towards the top-right. - **Intersections**: The curve crosses the x-axis (roots of the equation) at two points, indicating there are real roots. - **Central Feature**: The plot appears to be symmetric vertically about the point where it reaches its global minimum on the y-axis. - **Button**: Below the graph, there is an "OK" button, which suggests that the image might be from a software application or an online tool used for graphing or educational purposes. This graph can help students understand concepts like polynomial roots, turning points, and the behavior of quadratic or higher-degree polynomials.
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