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Give a formula for the transformation y = -k(x-4) of k(x) = 3⁰.

Give a formula for the transformation y = -k(x-4) of k(x) = 3⁰.

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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### Transformation of Exponential Functions **Objective:** Determine the formula and graphical transformation for a function \( y = -k(x-4) \) where \( k(x) = 3^x \). #### Formula Choices: To transform the function \( k(x) = 3^x \) using \( y = -k(x-4) \), select the correct modified equation: - \( -k(x-4) = 3^{-x-4} \) - \( -k(x-4) = -3^{x+4} \) - \( -k(x-4) = -3^{-x-4} \) - \( -k(x-4) = 3^{-x+4} \) - \( -k(x-4) = 3^{x+4} \) #### Graphical Transformation: **Task:** Given the graph of \( k(x) = 3^x \) in blue, identify the graph of the transformation \( y = -k(x-4) \) in green. - **Graph 1:** - Blue: Standard exponential growth curve. - Green: Reflection of the blue curve across the x-axis, shifted right by 4 units. - **Graph 2:** - Blue: Standard exponential growth curve. - Green: Reflection of the blue curve across the x-axis, with both vertical reflection and horizontal leftward shift. - **Graph 3:** - Blue: Standard exponential growth curve. - Green: Vertical reflection of the blue curve without horizontal shifting. - **Graph 4:** - Blue: Standard exponential growth curve. - Green: Horizontal shift left by 4 units and reflection across the x-axis. - **Graph 5:** - Blue: Standard exponential growth curve. - Green: Only shifted right by 4 units, without reflection. **Conclusion:** Identify and confirm which green graph accurately represents the transformation based on reflections and shifts.
Transcribed Image Text:### Transformation of Exponential Functions **Objective:** Determine the formula and graphical transformation for a function \( y = -k(x-4) \) where \( k(x) = 3^x \). #### Formula Choices: To transform the function \( k(x) = 3^x \) using \( y = -k(x-4) \), select the correct modified equation: - \( -k(x-4) = 3^{-x-4} \) - \( -k(x-4) = -3^{x+4} \) - \( -k(x-4) = -3^{-x-4} \) - \( -k(x-4) = 3^{-x+4} \) - \( -k(x-4) = 3^{x+4} \) #### Graphical Transformation: **Task:** Given the graph of \( k(x) = 3^x \) in blue, identify the graph of the transformation \( y = -k(x-4) \) in green. - **Graph 1:** - Blue: Standard exponential growth curve. - Green: Reflection of the blue curve across the x-axis, shifted right by 4 units. - **Graph 2:** - Blue: Standard exponential growth curve. - Green: Reflection of the blue curve across the x-axis, with both vertical reflection and horizontal leftward shift. - **Graph 3:** - Blue: Standard exponential growth curve. - Green: Vertical reflection of the blue curve without horizontal shifting. - **Graph 4:** - Blue: Standard exponential growth curve. - Green: Horizontal shift left by 4 units and reflection across the x-axis. - **Graph 5:** - Blue: Standard exponential growth curve. - Green: Only shifted right by 4 units, without reflection. **Conclusion:** Identify and confirm which green graph accurately represents the transformation based on reflections and shifts.
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