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Find the intercepts of f(x) = −2(x + 2)(x − 5)(x+4) . Enter intercepts as points. If you have more than one point, enter them as a comma separated list. ▪y-intercept: (0,80) help (points) ▪ x-intercept(s) (-2,0),(5,0),(-4,0), help (points)

Find the intercepts of f(x) = −2(x + 2)(x − 5)(x+4) . Enter intercepts as points. If you have more than one point, enter them as a comma separated list. ▪y-intercept: (0,80) help (points) ▪ x-intercept(s) (-2,0),(5,0),(-4,0), help (points)

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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**Finding Intercepts of a Polynomial Function** To find the intercepts of the function \( f(x) = -2(x + 2)(x - 5)(x + 4) \), follow these steps: **y-intercept:** - The y-intercept occurs where \( x = 0 \). - Substitute \( x = 0 \) into the function to find the y-coordinate of the intercept. - The y-intercept is: \( (0, 80) \). **x-intercepts:** - The x-intercepts occur where \( f(x) = 0 \). - Set the function equal to zero: \( -2(x + 2)(x - 5)(x + 4) = 0 \). - Solve for \( x \) by setting each factor equal to zero: - \( x + 2 = 0 \) gives \( x = -2 \) - \( x - 5 = 0 \) gives \( x = 5 \) - \( x + 4 = 0 \) gives \( x = -4 \) - The x-intercepts are: \( (-2, 0), (5, 0), (-4, 0) \). These steps help in determining where the graph of the function intersects the axes, which is essential for sketching the graph.
Transcribed Image Text:**Finding Intercepts of a Polynomial Function** To find the intercepts of the function \( f(x) = -2(x + 2)(x - 5)(x + 4) \), follow these steps: **y-intercept:** - The y-intercept occurs where \( x = 0 \). - Substitute \( x = 0 \) into the function to find the y-coordinate of the intercept. - The y-intercept is: \( (0, 80) \). **x-intercepts:** - The x-intercepts occur where \( f(x) = 0 \). - Set the function equal to zero: \( -2(x + 2)(x - 5)(x + 4) = 0 \). - Solve for \( x \) by setting each factor equal to zero: - \( x + 2 = 0 \) gives \( x = -2 \) - \( x - 5 = 0 \) gives \( x = 5 \) - \( x + 4 = 0 \) gives \( x = -4 \) - The x-intercepts are: \( (-2, 0), (5, 0), (-4, 0) \). These steps help in determining where the graph of the function intersects the axes, which is essential for sketching the graph.
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