### Understanding Exponential FunctionsAn 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](#)

Answered: Image /qna-images/answer/180961e2-1d7e-4b1a-bf18-aaab0f6a10c7.jpg

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

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)

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

### 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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