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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![**Title: Identifying the Equation of an Exponential Graph**
**Introduction:**
In this lesson, we will learn how to identify the equation of an exponential graph. You will see a graph plotted on the coordinate plane and we will discuss how to determine its corresponding mathematical equation.
**Graph Analysis:**
The given graph represents an exponential function. The x-axis ranges from -5 to 5, and the y-axis ranges from -8 to 8.
**Key Observations:**
1. The graph passes through the point (0, 0) and continues to rise steeply as x decreases and approaches negative infinity.
2. The graph approaches negative infinity along the y-axis as x increases.
3. There is a noticeable curved path indicating an exponential decay function, characterized by the sharp decline from a high positive value to approaching zero.
**Conclusion:**
For exponential functions of the form \( f(x) = a \cdot b^x \), where a is a coefficient and b is the base of the exponential (with \(0 < b < 1\) for decay), we observe that this particular graph represents a rapid decline.
**Task:**
Given the form of an exponential decay model, determine the specific equation that fits this graph. Use the following general format:
\[ f(x) = a \cdot b^x \]
* **Hint:** Consider the y-intercept and the rate at which the function decreases.
**Exercises:**
- Find specific points the graph passes through and use them to determine values for 'a' and 'b'.
- Verify your equation by checking if the graph passes through other points predicted by your function.
**Student Input:**
\[ f(x) = \text{___} \]
This hands-on activity will help solidify your understanding of how to translate graphical data into algebraic expressions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a66d878-2f58-4b17-a7a9-b61e2abefcf5%2F4ff68b41-a7a7-4d63-a3bc-5f61f70f5786%2Fjljpwq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Identifying the Equation of an Exponential Graph**
**Introduction:**
In this lesson, we will learn how to identify the equation of an exponential graph. You will see a graph plotted on the coordinate plane and we will discuss how to determine its corresponding mathematical equation.
**Graph Analysis:**
The given graph represents an exponential function. The x-axis ranges from -5 to 5, and the y-axis ranges from -8 to 8.
**Key Observations:**
1. The graph passes through the point (0, 0) and continues to rise steeply as x decreases and approaches negative infinity.
2. The graph approaches negative infinity along the y-axis as x increases.
3. There is a noticeable curved path indicating an exponential decay function, characterized by the sharp decline from a high positive value to approaching zero.
**Conclusion:**
For exponential functions of the form \( f(x) = a \cdot b^x \), where a is a coefficient and b is the base of the exponential (with \(0 < b < 1\) for decay), we observe that this particular graph represents a rapid decline.
**Task:**
Given the form of an exponential decay model, determine the specific equation that fits this graph. Use the following general format:
\[ f(x) = a \cdot b^x \]
* **Hint:** Consider the y-intercept and the rate at which the function decreases.
**Exercises:**
- Find specific points the graph passes through and use them to determine values for 'a' and 'b'.
- Verify your equation by checking if the graph passes through other points predicted by your function.
**Student Input:**
\[ f(x) = \text{___} \]
This hands-on activity will help solidify your understanding of how to translate graphical data into algebraic expressions.
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