**Piecewise Function Activity****Objective:** Express the function graphed on the axes as a piecewise function.**Graph Description:**- The graph is on a coordinate plane with x and y axes.- The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10.- There are two distinct segments in the graph: 1. A horizontal line at $ y = -6 $ extending leftwards from $ x = 0 $. This line includes an open circle at $ x = 0 $, indicating that the value is not included at this point. 2. A line with a positive slope starting from an open circle at $ (0, 2) $ and continuing diagonally upward through $ (5, 7) $.**Piecewise Function Representation:**Let $ f(x) $ be the piecewise function.- $ f(x) = -6 $ for $ x < 0 $- The values for the second segment of the piecewise function (for $ x \geq 0 $) need to be determined based on the graph's equation.To find the equation of the second line:- Identify two points on the line, such as $ (0,2) $ and $ (5,7) $.- Calculate the slope $ m = \frac{7 - 2}{5 - 0} = 1 $.- Use the point-slope form to find the equation: $ y - 2 = 1(x - 0) $.- Simplify to: $ y = x + 2 $.**Piecewise Function:**\[f(x) = \begin{cases} -6 & \text{for } x < 0 \\x + 2 & \text{for } x \geq 0\end{cases}\]Use the interactive tool to input your function rules and submit your answers.**Note:** Ensure accuracy in defining the domain for each segment.

Graph of the function is given, we have to find its equation.

Answered: Express the function graphed on the…

Express the function graphed on the axes below as a piecewise function. -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 y 10 9 8 7 6 5 4 3 2 1 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 1 2 3 4 5 6 7 8 9 10 X

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

**Piecewise Function Activity**

**Objective:** Express the function graphed on the axes as a piecewise function.

**Graph Description:**
- The graph is on a coordinate plane with x and y axes.
- The x-axis ranges from -10 to 10, and the y-axis ranges from -10 to 10.
- There are two distinct segments in the graph:
1. A horizontal line at $ y = -6 $ extending leftwards from $ x = 0 $. This line includes an open circle at $ x = 0 $, indicating that the value is not included at this point.
2. A line with a positive slope starting from an open circle at $ (0, 2) $ and continuing diagonally upward through $ (5, 7) $.

**Piecewise Function Representation:**

Let $ f(x) $ be the piecewise function.

- $ f(x) = -6 $ for $ x < 0 $
- The values for the second segment of the piecewise function (for $ x \geq 0 $) need to be determined based on the graph's equation.

To find the equation of the second line:
- Identify two points on the line, such as $ (0,2) $ and $ (5,7) $.
- Calculate the slope $ m = \frac{7 - 2}{5 - 0} = 1 $.
- Use the point-slope form to find the equation: $ y - 2 = 1(x - 0) $.
- Simplify to: $ y = x + 2 $.

**Piecewise Function:**

\[
f(x) =
\begin{cases}
-6 & \text{for } x < 0 \\
x + 2 & \text{for } x \geq 0
\end{cases}
\]

Use the interactive tool to input your function rules and submit your answers.

**Note:** Ensure accuracy in defining the domain for each segment.

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