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Draw the graph of f(x) = = 10-9-8-7-6-5-4-3-2 Clear All Draw: (3) ** 5 10+ 165 9 8 7+ t 6- 5. 3 2- 1 4 3371 29 -3 -4- -6- z+3 -7- -8- -9- -10+ 3 5 8 9 10

Draw the graph of f(x) = = 10-9-8-7-6-5-4-3-2 Clear All Draw: (3) ** 5 10+ 165 9 8 7+ t 6- 5. 3 2- 1 4 3371 29 -3 -4- -6- z+3 -7- -8- -9- -10+ 3 5 8 9 10

Algebra and Trigonometry (6th Edition)
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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Algebra Question 1/.6 

--- ### How to Graph Exponential Functions #### Task: Draw the Graph of \( f(x) = \left( \frac{1}{5} \right)^{x+3} \). #### Graph Overview The graph shown is a coordinate plane with a grid that extends from -10 to 10 on both the x-axis and y-axis. The axes intersect at the origin (0,0). #### Steps to Graph 1. **Identify the base and transformation**: - The base of the exponential function is \( \frac{1}{5} \), indicating it is a decreasing exponential function. - The function \( f(x) = \left( \frac{1}{5} \right)^{x+3} \) includes a horizontal shift left by 3 units. 2. **Plot key points**: - Calculate and plot a few points to help graph the curve. - For example, choose values of \( x \), calculate \( f(x) \), and then plot the points \((-3, 1)\), \(-2, f(x)\), etc. 3. **Draw the curve**: - Sketch the curve, noting that because the base is less than 1, the function will decrease as \( x \) increases. - The curve should approach the x-axis as an asymptote but never actually touch it. #### Interactive Features - **Clear All**: This button clears the current drawing, allowing you to start over. - **Draw Tool**: Use this tool to manually draw the function on the grid. This approach will help in understanding the characteristics of an exponential function and its graph transformation. ---
Transcribed Image Text:--- ### How to Graph Exponential Functions #### Task: Draw the Graph of \( f(x) = \left( \frac{1}{5} \right)^{x+3} \). #### Graph Overview The graph shown is a coordinate plane with a grid that extends from -10 to 10 on both the x-axis and y-axis. The axes intersect at the origin (0,0). #### Steps to Graph 1. **Identify the base and transformation**: - The base of the exponential function is \( \frac{1}{5} \), indicating it is a decreasing exponential function. - The function \( f(x) = \left( \frac{1}{5} \right)^{x+3} \) includes a horizontal shift left by 3 units. 2. **Plot key points**: - Calculate and plot a few points to help graph the curve. - For example, choose values of \( x \), calculate \( f(x) \), and then plot the points \((-3, 1)\), \(-2, f(x)\), etc. 3. **Draw the curve**: - Sketch the curve, noting that because the base is less than 1, the function will decrease as \( x \) increases. - The curve should approach the x-axis as an asymptote but never actually touch it. #### Interactive Features - **Clear All**: This button clears the current drawing, allowing you to start over. - **Draw Tool**: Use this tool to manually draw the function on the grid. This approach will help in understanding the characteristics of an exponential function and its graph transformation. ---
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