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The graph of y = f(x) is given. Graph the function y =2f (x-3)+1. 3- 2- y = = f(x)

The graph of y = f(x) is given. Graph the function y =2f (x-3)+1. 3- 2- y = = f(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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The text reads: "The graph of \( y = f(x) \) is given. Graph the function \( y = 2f(x-3) + 1 \)." The image shows a coordinate plane with the graph of the function \( y = f(x) \) plotted. The graph appears to be a smooth curve starting at approximately (-3, 0) moving upwards to (0, approximately -1), then downwards to (1.5, 0), peaking at (2, about 2), and continuing on in a typical oscillating or wave-like pattern. Key features of the graph: - The graph is centered on the origin with equal scales on the x and y axes. - The oscillations suggest the graph could represent a trigonometric or smooth polynomial function. The task requests a new graph to be drawn for the function \( y = 2f(x-3) + 1 \), which involves: - **Horizontal Shift:** The function \( f(x-3) \) shifts the original graph 3 units to the right. - **Vertical Scaling and Reflection:** The function \( 2f(x-3) \) stretches the graph vertically by a factor of 2, effectively doubling the distance of each point from the x-axis. - **Vertical Shift:** Adding 1 to the result, \( 2f(x-3) + 1 \) shifts the entire graph up by 1 unit. These transformations will produce a new graph that retains the shape of \( f(x) \) but repositioned according to these transformations.
Transcribed Image Text:The text reads: "The graph of \( y = f(x) \) is given. Graph the function \( y = 2f(x-3) + 1 \)." The image shows a coordinate plane with the graph of the function \( y = f(x) \) plotted. The graph appears to be a smooth curve starting at approximately (-3, 0) moving upwards to (0, approximately -1), then downwards to (1.5, 0), peaking at (2, about 2), and continuing on in a typical oscillating or wave-like pattern. Key features of the graph: - The graph is centered on the origin with equal scales on the x and y axes. - The oscillations suggest the graph could represent a trigonometric or smooth polynomial function. The task requests a new graph to be drawn for the function \( y = 2f(x-3) + 1 \), which involves: - **Horizontal Shift:** The function \( f(x-3) \) shifts the original graph 3 units to the right. - **Vertical Scaling and Reflection:** The function \( 2f(x-3) \) stretches the graph vertically by a factor of 2, effectively doubling the distance of each point from the x-axis. - **Vertical Shift:** Adding 1 to the result, \( 2f(x-3) + 1 \) shifts the entire graph up by 1 unit. These transformations will produce a new graph that retains the shape of \( f(x) \) but repositioned according to these transformations.
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