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The graph of the function f(x) 4x4 12x3 x + 7x – 3 is shown below. | 30+ 25 20- 15 10- 5 -6 -5-4-3 |-2 to 4- -10- -15- +20 -25- +30- a. Enter the monomial expression that best estimates the value of f(x) as x → ± ∞. Preview

The graph of the function f(x) 4x4 12x3 x + 7x – 3 is shown below. | 30+ 25 20- 15 10- 5 -6 -5-4-3 |-2 to 4- -10- -15- +20 -25- +30- a. Enter the monomial expression that best estimates the value of f(x) as x → ± ∞. Preview

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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**Graph of the Function** This section presents the graph of the polynomial function: \[ f(x) = 4x^4 - 12x^3 - x^2 + 7x - 3 \] ### Graph Description - **Axes**: The graph is plotted on a coordinate system with both the x-axis and y-axis labeled and scaled. The x-axis ranges from -6 to 6, and the y-axis ranges from -30 to 30. - **Shape**: The graph depicts a quartic polynomial, which generally has a "W" or "M" shape due to its degree of four. It demonstrates fluctuations with local maxima and minima. - **Behavior**: The graph shows significant behavior changes around the x-values where it switches direction, indicating probable turning points. - **Intercepts**: The approximate x-intercepts can be identified, though the exact values would require solving the function algebraically. The y-intercept occurs at the point where the function crosses the y-axis. ### Problem Statement a. **Task**: Enter the monomial expression that best estimates the value of \( f(x) \) as \( x \to \pm \infty \). This involves deducing the dominant term of the polynomial, which influences the end behavior of the graph. Typically, as \( x \to \infty \) or \( x \to -\infty \), the highest power of \( x \) determines the function's growth behavior. **Input Box**: An input box is provided for students to enter their answer, which will be verified upon clicking the "Preview" button.
Transcribed Image Text:**Graph of the Function** This section presents the graph of the polynomial function: \[ f(x) = 4x^4 - 12x^3 - x^2 + 7x - 3 \] ### Graph Description - **Axes**: The graph is plotted on a coordinate system with both the x-axis and y-axis labeled and scaled. The x-axis ranges from -6 to 6, and the y-axis ranges from -30 to 30. - **Shape**: The graph depicts a quartic polynomial, which generally has a "W" or "M" shape due to its degree of four. It demonstrates fluctuations with local maxima and minima. - **Behavior**: The graph shows significant behavior changes around the x-values where it switches direction, indicating probable turning points. - **Intercepts**: The approximate x-intercepts can be identified, though the exact values would require solving the function algebraically. The y-intercept occurs at the point where the function crosses the y-axis. ### Problem Statement a. **Task**: Enter the monomial expression that best estimates the value of \( f(x) \) as \( x \to \pm \infty \). This involves deducing the dominant term of the polynomial, which influences the end behavior of the graph. Typically, as \( x \to \infty \) or \( x \to -\infty \), the highest power of \( x \) determines the function's growth behavior. **Input Box**: An input box is provided for students to enter their answer, which will be verified upon clicking the "Preview" button.
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