7. Start from the given graph of y = log5 (x), then sketch the graph of the following function. f(x) = log5 (x-1) + 1 Sketch the vertical asymptote and mark at least one relevant point on the graph.
7. Start from the given graph of y = log5 (x), then sketch the graph of the following function. f(x) = log5 (x-1) + 1 Sketch the vertical asymptote and mark at least one relevant point on the graph.
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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![### Problem 7:
**Task:** Start from the given graph of \( y = \log_5(x) \), then sketch the graph of the following function.
\[ f(x) = \log_5(x - 1) + 1 \]
**Instructions:** Sketch the vertical asymptote and mark at least one relevant point on the graph.
**Graph Description:**
- The graph provided shows the function \( f(x) = \log_5(x - 1) + 1 \).
- The curve starts from just above the x-axis and increases slowly, moving to the right.
- There is a vertical asymptote at \( x = 1 \), where the function is undefined.
**Additional Requirements:**
- State the domain, the range, and the asymptote of the function using interval notation.
**Answers:**
- **Domain:** \( (1, \infty) \)
- **Range:** \( (-\infty, \infty) \)
- **Asymptote:** \( x = 1 \)
Ensure your sketch accurately represents the position and nature of the asymptote and includes at least one relevant point on the curve to demonstrate understanding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F076cf337-ca04-4cd7-8e92-fdbadf0d0ca6%2Ff491f9f0-f7a1-4533-9861-99e78cd8afc0%2Fkysmlvy_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 7:
**Task:** Start from the given graph of \( y = \log_5(x) \), then sketch the graph of the following function.
\[ f(x) = \log_5(x - 1) + 1 \]
**Instructions:** Sketch the vertical asymptote and mark at least one relevant point on the graph.
**Graph Description:**
- The graph provided shows the function \( f(x) = \log_5(x - 1) + 1 \).
- The curve starts from just above the x-axis and increases slowly, moving to the right.
- There is a vertical asymptote at \( x = 1 \), where the function is undefined.
**Additional Requirements:**
- State the domain, the range, and the asymptote of the function using interval notation.
**Answers:**
- **Domain:** \( (1, \infty) \)
- **Range:** \( (-\infty, \infty) \)
- **Asymptote:** \( x = 1 \)
Ensure your sketch accurately represents the position and nature of the asymptote and includes at least one relevant point on the curve to demonstrate understanding.
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