**Title: Finding the Equation for the Exponential Graph** **Problem Statement:** "Find an equation for the graph sketched below." **Graph Description:** The graph is a typical exponential curve that increases rapidly as it moves to the right. The curve starts from the lower-left quadrant and rises steeply in the right quadrant. It appears to be an exponential function, possibly of the form \( f(x) = a \cdot b^x \), where \( a \) and \( b \) are constants, and \( b > 1 \). - The y-axis ranges approximately from -6 to 8. - The x-axis ranges approximately from -5 to 5. - The curve is asymptotic to the x-axis in the negative direction and rises sharply in the positive direction. **Instructions:** There is a section labeled \( f(x) = \) for inputting the derived equation. **Additional Resources:** - "Get help: Video" is provided for further assistance. **Analysis:** To find the equation of the graph: 1. **Determine the form of the equation**: Considering the rapid increase, the equation is likely exponential. 2. **Identify Points on the Graph**: Choose points the graph passes through to find specific values for constants \( a \) and \( b \). 3. **Solve for Constants**: Use simultaneous equations if necessary to determine the exact exponential function. **Conclusion:** By analyzing the curve’s characteristics, such as its rapid increase and asymptotic behavior, one can derive the corresponding exponential equation for the given graph.
**Title: Finding the Equation for the Exponential Graph** **Problem Statement:** "Find an equation for the graph sketched below." **Graph Description:** The graph is a typical exponential curve that increases rapidly as it moves to the right. The curve starts from the lower-left quadrant and rises steeply in the right quadrant. It appears to be an exponential function, possibly of the form \( f(x) = a \cdot b^x \), where \( a \) and \( b \) are constants, and \( b > 1 \). - The y-axis ranges approximately from -6 to 8. - The x-axis ranges approximately from -5 to 5. - The curve is asymptotic to the x-axis in the negative direction and rises sharply in the positive direction. **Instructions:** There is a section labeled \( f(x) = \) for inputting the derived equation. **Additional Resources:** - "Get help: Video" is provided for further assistance. **Analysis:** To find the equation of the graph: 1. **Determine the form of the equation**: Considering the rapid increase, the equation is likely exponential. 2. **Identify Points on the Graph**: Choose points the graph passes through to find specific values for constants \( a \) and \( b \). 3. **Solve for Constants**: Use simultaneous equations if necessary to determine the exact exponential function. **Conclusion:** By analyzing the curve’s characteristics, such as its rapid increase and asymptotic behavior, one can derive the corresponding exponential equation for the given graph.
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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Transcribed Image Text:**Title: Finding the Equation for the Exponential Graph**
**Problem Statement:**
"Find an equation for the graph sketched below."
**Graph Description:**
The graph is a typical exponential curve that increases rapidly as it moves to the right. The curve starts from the lower-left quadrant and rises steeply in the right quadrant. It appears to be an exponential function, possibly of the form \( f(x) = a \cdot b^x \), where \( a \) and \( b \) are constants, and \( b > 1 \).
- The y-axis ranges approximately from -6 to 8.
- The x-axis ranges approximately from -5 to 5.
- The curve is asymptotic to the x-axis in the negative direction and rises sharply in the positive direction.
**Instructions:**
There is a section labeled \( f(x) = \) for inputting the derived equation.
**Additional Resources:**
- "Get help: Video" is provided for further assistance.
**Analysis:**
To find the equation of the graph:
1. **Determine the form of the equation**: Considering the rapid increase, the equation is likely exponential.
2. **Identify Points on the Graph**: Choose points the graph passes through to find specific values for constants \( a \) and \( b \).
3. **Solve for Constants**: Use simultaneous equations if necessary to determine the exact exponential function.
**Conclusion:**
By analyzing the curve’s characteristics, such as its rapid increase and asymptotic behavior, one can derive the corresponding exponential equation for the given graph.
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