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Use the graph of y = f(x) shown to the right to graph the following function g. y=f(x), Ay 1 g(x) = (x + 4)- 2

Use the graph of y = f(x) shown to the right to graph the following function g. y=f(x), Ay 1 g(x) = (x + 4)- 2

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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Use the graph of \( y = f(x) \) shown to the right to graph the following function \( g \): \[ g(x) = -\frac{1}{2} f(x+4) - 2 \] Choose the correct graph below: - Option A - Option B - Option C - Option D **Graph Description:** 1. **Reference Graph (Top Right):** - This graph represents \( y = f(x) \). It is labeled with the axes \( x \) and \( y \), and shows the curve or line representing the function \( f(x) \). 2. **Options A, B, C, and D (Bottom):** - Each option shows a graph on a grid with axes labeled \( x \) and \( y \). - The graphs differ in the position and orientation of the function curve, displaying possible results of the transformation applied to \( f(x) \) as given by \( g(x) = -\frac{1}{2} f(x+4) - 2 \). **Explanation of Transformation:** The transformation of the function \( f(x) \) to \( g(x) \) involves: - **Horizontal Shift:** \( f(x+4) \) indicates a shift to the left by 4 units. - **Vertical Stretch and Reflection:** The multiplication by \(-\frac{1}{2}\) reflects the graph across the x-axis and scales it vertically by a factor of \(\frac{1}{2}\). - **Vertical Shift:** The subtraction of 2 shifts the graph downwards by 2 units. Selecting the correct graph involves identifying these transformations in the options provided.
Transcribed Image Text:Use the graph of \( y = f(x) \) shown to the right to graph the following function \( g \): \[ g(x) = -\frac{1}{2} f(x+4) - 2 \] Choose the correct graph below: - Option A - Option B - Option C - Option D **Graph Description:** 1. **Reference Graph (Top Right):** - This graph represents \( y = f(x) \). It is labeled with the axes \( x \) and \( y \), and shows the curve or line representing the function \( f(x) \). 2. **Options A, B, C, and D (Bottom):** - Each option shows a graph on a grid with axes labeled \( x \) and \( y \). - The graphs differ in the position and orientation of the function curve, displaying possible results of the transformation applied to \( f(x) \) as given by \( g(x) = -\frac{1}{2} f(x+4) - 2 \). **Explanation of Transformation:** The transformation of the function \( f(x) \) to \( g(x) \) involves: - **Horizontal Shift:** \( f(x+4) \) indicates a shift to the left by 4 units. - **Vertical Stretch and Reflection:** The multiplication by \(-\frac{1}{2}\) reflects the graph across the x-axis and scales it vertically by a factor of \(\frac{1}{2}\). - **Vertical Shift:** The subtraction of 2 shifts the graph downwards by 2 units. Selecting the correct graph involves identifying these transformations in the options provided.
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