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
### Description of the Graph
The image contains a Cartesian coordinate graph with the x-axis ranging approximately from -5 to 7 and the y-axis ranging approximately from -5 to 7. The graph features a red curve that exhibits the following behavior:
- The curve starts from negative infinity as x approaches 2 from the left.
- It approaches y = 1 as x gets larger, but it never touches y = 1, suggesting a horizontal asymptote at y = 1.
- It also has a vertical asymptote at x = 2, where the function is undefined.
### Possible Equations
1. \( y = (x - 2)^2 - 1 \)
2. \( y = \frac{1}{(x - 2)} + 1 \)
3. \( y = (x - 2)^3 + 1 \)
4. \( y = \sqrt{(x - 2)} + 1 \)
### Correct Answer
\[ \boxed{y = \frac{1}{(x - 2)} + 1} \]
This equation aligns with the observed behavior of the graph, indicating that the function has both vertical and horizontal asymptotes where described. The other equations do not exhibit the same characteristics as the graph shown.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce57007f-4539-4532-9ec0-65e156785b7b%2Fec4268bb-02a2-457f-8f47-98093d57b0bd%2Fcbxgrut_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question
**What is the equation of the following equation?**
### Description of the Graph
The image contains a Cartesian coordinate graph with the x-axis ranging approximately from -5 to 7 and the y-axis ranging approximately from -5 to 7. The graph features a red curve that exhibits the following behavior:
- The curve starts from negative infinity as x approaches 2 from the left.
- It approaches y = 1 as x gets larger, but it never touches y = 1, suggesting a horizontal asymptote at y = 1.
- It also has a vertical asymptote at x = 2, where the function is undefined.
### Possible Equations
1. \( y = (x - 2)^2 - 1 \)
2. \( y = \frac{1}{(x - 2)} + 1 \)
3. \( y = (x - 2)^3 + 1 \)
4. \( y = \sqrt{(x - 2)} + 1 \)
### Correct Answer
\[ \boxed{y = \frac{1}{(x - 2)} + 1} \]
This equation aligns with the observed behavior of the graph, indicating that the function has both vertical and horizontal asymptotes where described. The other equations do not exhibit the same characteristics as the graph shown.
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