### Explanation of the Piecewise-Defined Function GraphThe task asks us to draw the graph of \( g(x) = f(x+5) - 1 \) based on the given graph of the piecewise-defined function \( f(x) \).#### Graph Description:- **Original Function \( f(x) \)**: - The graph is shown on a coordinate plane with the horizontal axis ranging from -7 to 7 and the vertical axis ranging from -3 to 9. - The function consists of three segments: 1. A horizontal line from \((0, 3)\) to \((2, 0)\) (descending). 2. A dashed line from \((2, 0)\) to \((3, 2)\). 3. Another horizontal line from \((3, 2)\) to \((5, 3)\).#### Steps to Transform \( f(x) \) to \( g(x) = f(x + 5) - 1 \):1. **Horizontal Shift**: Replace \( x \) with \( x + 5 \) to shift the graph 5 units to the left.2. **Vertical Shift**: Subtract 1 from the function, shifting the entire graph down by 1 unit.By applying these transformations, the new graph \( g(x) \) will appear differently on the coordinate plane, following the shifts for the x-values and reducing the y-values by 1.

The graph of the piecewise-defined function, f(x), is shown on the coordinate plane below. Draw what the graph of g(x)=f(x+5)-1 would look like. 2 T ERASER SMALL -5 A -రు. -2 -1 8 7 6 -5 4 1 0 -1 1 2 3 4 5 B

The graph of the piecewise-defined function, f(x), is shown on the coordinate plane below. Draw what the graph of g(x)=f(x+5)-1 would look like. 2 T ERASER SMALL -5 A -రు. -2 -1 8 7 6 -5 4 1 0 -1 1 2 3 4 5 B

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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Question

### Explanation of the Piecewise-Defined Function Graph

The task asks us to draw the graph of \( g(x) = f(x+5) - 1 \) based on the given graph of the piecewise-defined function \( f(x) \).

#### Graph Description:
- **Original Function \( f(x) \)**:
- The graph is shown on a coordinate plane with the horizontal axis ranging from -7 to 7 and the vertical axis ranging from -3 to 9.
- The function consists of three segments:
1. A horizontal line from \((0, 3)\) to \((2, 0)\) (descending).
2. A dashed line from \((2, 0)\) to \((3, 2)\).
3. Another horizontal line from \((3, 2)\) to \((5, 3)\).

#### Steps to Transform \( f(x) \) to \( g(x) = f(x + 5) - 1 \):
1. **Horizontal Shift**: Replace \( x \) with \( x + 5 \) to shift the graph 5 units to the left.
2. **Vertical Shift**: Subtract 1 from the function, shifting the entire graph down by 1 unit.

By applying these transformations, the new graph \( g(x) \) will appear differently on the coordinate plane, following the shifts for the x-values and reducing the y-values by 1.

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