Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
![**Graph and Function Matching Exercise**
**Topic: Logarithmic Functions**
**Instruction:**
Choose the function to match the graph.
**Graph Analysis:**
The graph displayed is a logarithmic curve. The red curve starts from the far left and rises steeply, leveling off more gradually as it moves to the right. This shape is characteristic of a logarithmic function, which generally has the form \( f(x) = \log(x - a) \), where \( a \) shifts the graph horizontally.
In this specific graph:
- As \( x \) increases from 6 to the right, the graph increases gradually.
- Prior to \( x = 5 \), the graph drastically decreases as it approaches a vertical asymptote at \( x = 5 \).
**Function Options:**
1. \( f(x) = \log(x + 5) \)
2. \( f(x) = \log(x - 5) \)
3. \( f(x) = \log(x + 5) \)
4. \( f(x) = \log(x - 5) \)
Since the vertical asymptote is at \( x = 5 \), the correct function representing this behavior is:
\[ f(x) = \log(x - 5) \]
Thus, select the second or fourth option in the list, both corresponding to the function \( f(x) = \log(x - 5) \).
**Educational Objective:**
Understanding how logarithmic functions are graphed and knowing how to identify their transformations, in this case, horizontal shifts, by accurately associating the function with its corresponding graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F355372c0-0b06-4568-8d9a-cddd4364f7ea%2F7c9c9f8b-c341-40bd-97e0-bbbb1b77c123%2F8cbotxe_processed.png&w=3840&q=75)
Transcribed Image Text:**Graph and Function Matching Exercise**
**Topic: Logarithmic Functions**
**Instruction:**
Choose the function to match the graph.
**Graph Analysis:**
The graph displayed is a logarithmic curve. The red curve starts from the far left and rises steeply, leveling off more gradually as it moves to the right. This shape is characteristic of a logarithmic function, which generally has the form \( f(x) = \log(x - a) \), where \( a \) shifts the graph horizontally.
In this specific graph:
- As \( x \) increases from 6 to the right, the graph increases gradually.
- Prior to \( x = 5 \), the graph drastically decreases as it approaches a vertical asymptote at \( x = 5 \).
**Function Options:**
1. \( f(x) = \log(x + 5) \)
2. \( f(x) = \log(x - 5) \)
3. \( f(x) = \log(x + 5) \)
4. \( f(x) = \log(x - 5) \)
Since the vertical asymptote is at \( x = 5 \), the correct function representing this behavior is:
\[ f(x) = \log(x - 5) \]
Thus, select the second or fourth option in the list, both corresponding to the function \( f(x) = \log(x - 5) \).
**Educational Objective:**
Understanding how logarithmic functions are graphed and knowing how to identify their transformations, in this case, horizontal shifts, by accurately associating the function with its corresponding graph.
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