**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.

Here Function value is 0 at x=6 , (from Graph) and we know that log(1)=0 so at x=6, log(x-5)…

Answered: Choose the function to match the graph.…

Choose the function to match the graph. Of(x) = log x + 5 Of(x) = log x-5 f(x) = log (x + 5) Of(x) = log (x - 5) 1 $ 12 15 N

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.

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