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Determine which graph represtents the shift in the indicated equation, where y=f(x). y=f(x-4)-5 O A. Q B. Q O C. Q N O

Determine which graph represtents the shift in the indicated equation, where y=f(x). y=f(x-4)-5 O A. Q B. Q O C. Q N O

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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**Determine which graph represents the shift in the indicated equation, where \( y = f(x) \).** **Equation:** \( y = f(x - 4) - 5 \) The task is to identify the graph that correctly shows the transformation described by the equation. This involves two transformations applied to the parent function \( y = f(x) \): 1. **Horizontal Shift:** \( x - 4 \) indicates a shift to the right by 4 units. 2. **Vertical Shift:** Subtracting 5 indicates a downward shift by 5 units. **Graphs:** - **Graph A:** This graph shows a parabola that has shifted horizontally to the left and vertically upwards. - **Graph B:** This graph shows a parabola that has shifted horizontally to the left and vertically downwards. - **Graph C:** This graph displays a parabola that has shifted horizontally to the right and vertically downwards, matching the described transformation. - **Graph D:** This graph shows a parabola that has shifted horizontally to the right and vertically upwards. **Correct Graph:** **C** Graph C correctly represents the shift described by \( y = f(x - 4) - 5 \), with a rightward shift of 4 units and a downward shift of 5 units.
Transcribed Image Text:**Determine which graph represents the shift in the indicated equation, where \( y = f(x) \).** **Equation:** \( y = f(x - 4) - 5 \) The task is to identify the graph that correctly shows the transformation described by the equation. This involves two transformations applied to the parent function \( y = f(x) \): 1. **Horizontal Shift:** \( x - 4 \) indicates a shift to the right by 4 units. 2. **Vertical Shift:** Subtracting 5 indicates a downward shift by 5 units. **Graphs:** - **Graph A:** This graph shows a parabola that has shifted horizontally to the left and vertically upwards. - **Graph B:** This graph shows a parabola that has shifted horizontally to the left and vertically downwards. - **Graph C:** This graph displays a parabola that has shifted horizontally to the right and vertically downwards, matching the described transformation. - **Graph D:** This graph shows a parabola that has shifted horizontally to the right and vertically upwards. **Correct Graph:** **C** Graph C correctly represents the shift described by \( y = f(x - 4) - 5 \), with a rightward shift of 4 units and a downward shift of 5 units.
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