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at least 9. Graph four steps, y = [x] also called y = int(x)

at least 9. Graph four steps, y = [x] also called y = int(x)

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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**Question 9:** Graph at least four steps for the function \( y = \left\lfloor x \right\rfloor \), also called \( y = \text{int}(x) \). **Explanation:** The function \( y = \left\lfloor x \right\rfloor \), known as the floor function or greatest integer function, outputs the greatest integer less than or equal to \( x \). The graph of this function is a step function, characterized by horizontal line segments that are open on the left and closed on the right at each integer \( x \). To construct the graph: - For each integer \( n \), plot a horizontal line segment from \( (n, n) \) to \( (n+1, n) \), with an open circle at \( (n+1, n) \). - Repeat this process for at least four steps to capture the basic shape and nature of the floor function.
Transcribed Image Text:**Question 9:** Graph at least four steps for the function \( y = \left\lfloor x \right\rfloor \), also called \( y = \text{int}(x) \). **Explanation:** The function \( y = \left\lfloor x \right\rfloor \), known as the floor function or greatest integer function, outputs the greatest integer less than or equal to \( x \). The graph of this function is a step function, characterized by horizontal line segments that are open on the left and closed on the right at each integer \( x \). To construct the graph: - For each integer \( n \), plot a horizontal line segment from \( (n, n) \) to \( (n+1, n) \), with an open circle at \( (n+1, n) \). - Repeat this process for at least four steps to capture the basic shape and nature of the floor function.
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