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Draw the graph of y = 4*, then use it to draw the graph of y= log4(x). y

Draw the graph of y = 4*, then use it to draw the graph of y= log4(x). y

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
**Graph Analysis of \( y = 4^x \) and \( y = \log_4(x) \)** In the given task, we are asked to draw the graph of \( y = 4^x \) and use it to graph \( y = \log_4(x) \). Below is an explanation of each graph shown in the images: 1. **Top Left Graph:** - The graph of \( y = 4^x \) is in blue. - The graph of \( y = \log_4(x) \) is in black. - A diagonal line \( y = x \) is shown as a dotted line, representing the line of reflection. - The \( y = \log_4(x) \) function appears to be reflected incorrectly. 2. **Top Right Graph:** - The graph of \( y = 4^x \) is in blue. - The graph of \( y = \log_4(x) \) is in black. - The diagonal line \( y = x \) connects points symmetrically from both curves as intended. - This graph correctly represents the relationship, showing the functions as reflections over the line \( y = x \), indicating they are inverses. 3. **Bottom Left Graph:** - The graph of \( y = 4^x \) is in blue. - The graph of \( y = \log_4(x) \) is in black. - The reflection over the line \( y = x \) is not correct here, as the shapes do not match over this line. 4. **Bottom Right Graph:** - The graph of \( y = 4^x \) is in blue. - The graph of \( y = \log_4(x) \) is in black. - Like the top right graph, this one aligns well with the line of reflection \( y = x \), properly showing the inverse relationship. **Conclusion:** The correct visualization of the graphs for \( y = 4^x \) and \( y = \log_4(x) \) recognizes their relationship as inverses. The top right and bottom right graphs depict this accurately through symmetrical reflection over the line \( y = x \).
Transcribed Image Text:**Graph Analysis of \( y = 4^x \) and \( y = \log_4(x) \)** In the given task, we are asked to draw the graph of \( y = 4^x \) and use it to graph \( y = \log_4(x) \). Below is an explanation of each graph shown in the images: 1. **Top Left Graph:** - The graph of \( y = 4^x \) is in blue. - The graph of \( y = \log_4(x) \) is in black. - A diagonal line \( y = x \) is shown as a dotted line, representing the line of reflection. - The \( y = \log_4(x) \) function appears to be reflected incorrectly. 2. **Top Right Graph:** - The graph of \( y = 4^x \) is in blue. - The graph of \( y = \log_4(x) \) is in black. - The diagonal line \( y = x \) connects points symmetrically from both curves as intended. - This graph correctly represents the relationship, showing the functions as reflections over the line \( y = x \), indicating they are inverses. 3. **Bottom Left Graph:** - The graph of \( y = 4^x \) is in blue. - The graph of \( y = \log_4(x) \) is in black. - The reflection over the line \( y = x \) is not correct here, as the shapes do not match over this line. 4. **Bottom Right Graph:** - The graph of \( y = 4^x \) is in blue. - The graph of \( y = \log_4(x) \) is in black. - Like the top right graph, this one aligns well with the line of reflection \( y = x \), properly showing the inverse relationship. **Conclusion:** The correct visualization of the graphs for \( y = 4^x \) and \( y = \log_4(x) \) recognizes their relationship as inverses. The top right and bottom right graphs depict this accurately through symmetrical reflection over the line \( y = x \).
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