An exponential function is of the form v(x) = b + C which is shown in the graph. Which of the following must be true of the parameter b or c? -10 -8 -6 -4-2 10₁ 8 6 4 2 -2 -6 -8 -10 2 +- 4 6 8 10 The parameter b must be 0; b = 0 The parameter c must be -6; c = -6 The parameter c must be 2; c = 2 The parameter b must be 0.5; b = 0.5

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Understanding Exponential Functions

An exponential function is of the form \( v(x) = b^x + c \) as shown in the graph below. We need to determine which of the following statements is true about the parameter \( b \) or \( c \):

#### Options:
1. The parameter \( b \) must be 0; \( b = 0 \)
2. The parameter \( c \) must be -6; \( c = -6 \)
3. The parameter \( c \) must be 2; \( c = 2 \)
4. The parameter \( b \) must be 0.5; \( b = 0.5 \)

#### Graph Analysis:
The provided graph displays an exponential function with the y-axis ranging from -10 to 10 and the x-axis from -10 to 10. The graph passes through the coordinates \( (0, -6) \) indicating that when \( x = 0 \), \( v(x) = -6 \).

![Graph](image-link)

### Explanation:
After examining the graph, we notice an essential behavior characteristic of exponential functions, especially where the graph passes through key points and the behavior as \( x \) approaches positive and negative infinity.

In this case:
- The parameter \( c \) adjusts the vertical shift of the graph. Since the function passes through \( (0, -6) \), it indicates that \( c \) must be -6.

### Correct Answer:
The parameter \( c \) must be -6; \( c = -6 \). 

### Additional Resources:
- [Exponential Function Basics](#)
- [Understanding Parameters in Exponential Functions](#)
Transcribed Image Text:### Understanding Exponential Functions An exponential function is of the form \( v(x) = b^x + c \) as shown in the graph below. We need to determine which of the following statements is true about the parameter \( b \) or \( c \): #### Options: 1. The parameter \( b \) must be 0; \( b = 0 \) 2. The parameter \( c \) must be -6; \( c = -6 \) 3. The parameter \( c \) must be 2; \( c = 2 \) 4. The parameter \( b \) must be 0.5; \( b = 0.5 \) #### Graph Analysis: The provided graph displays an exponential function with the y-axis ranging from -10 to 10 and the x-axis from -10 to 10. The graph passes through the coordinates \( (0, -6) \) indicating that when \( x = 0 \), \( v(x) = -6 \). ![Graph](image-link) ### Explanation: After examining the graph, we notice an essential behavior characteristic of exponential functions, especially where the graph passes through key points and the behavior as \( x \) approaches positive and negative infinity. In this case: - The parameter \( c \) adjusts the vertical shift of the graph. Since the function passes through \( (0, -6) \), it indicates that \( c \) must be -6. ### Correct Answer: The parameter \( c \) must be -6; \( c = -6 \). ### Additional Resources: - [Exponential Function Basics](#) - [Understanding Parameters in Exponential Functions](#)
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