### Graphing Piecewise Functions**Instructions:**Graph the following piecewise function:\[ f(x) = \begin{cases} -2 & \text{if } x \leq 2 \\-1 & \text{if } x > 2 \end{cases} \]**Choose the correct graph from the options below:**#### Options:1. **Option A:** - This graph shows a line segment where $ f(x) = -2 $ for $ x \leq 2 $ and a horizontal line at $ f(x) = -1 $ for $ x > 2 $. - It is characterized by a solid dot at the point (2, -2) and an open dot at the point (2, -1), indicating the function changes from -2 to -1 exactly at $ x = 2 $.2. **Option B:** - This graph displays a line segment at $ f(x) = -1 $ for $ x \leq 2 $ and a horizontal line at $ f(x) = -2 $ for $ x > 2 $. - Solid and open dots are swapped, which does not match the conditions given.3. **Option C:** - This graph illustrates a line where $ f(x) = -2 $ over all $ x $, which does not match the piecewise function.4. **Option D:** - This graph demonstrates a line where $ f(x) = -1 $ for all $ x $, not accurately representing the piecewise nature of the function.### Solution Explanation:The correct graph needs to reflect two segments;- A horizontal line segment at $ f(x) = -2 $ extending up to and including $ x = 2 $.- Another horizontal line segment at $ f(x) = -1 $ starting just after $ x = 2 $.Thus:- The correct graph is **Option A**. - This graph correctly shows: - A solid dot at (2, -2), indicating the function's value is -2 at $ x = 2 $. - An open dot at (2, -1), indicating the function's value immediately changes to -1 for $ x > 2 $.This detailed explanation should help you understand how to graph piecewise functions and identify the correct

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Answered: Graph the following piecewise function.…

Math

Algebra

Graph the following piecewise function. -2 if xs2 f(x) = -1 if x>2 Choose the correct graph below. A. O B. C.

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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Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

### Graphing Piecewise Functions

**Instructions:**

Graph the following piecewise function:

\[ f(x) = \begin{cases}
-2 & \text{if } x \leq 2 \\
-1 & \text{if } x > 2
\end{cases} \]

**Choose the correct graph from the options below:**

#### Options:

1. **Option A:**
- This graph shows a line segment where $ f(x) = -2 $ for $ x \leq 2 $ and a horizontal line at $ f(x) = -1 $ for $ x > 2 $.
- It is characterized by a solid dot at the point (2, -2) and an open dot at the point (2, -1), indicating the function changes from -2 to -1 exactly at $ x = 2 $.

2. **Option B:**
- This graph displays a line segment at $ f(x) = -1 $ for $ x \leq 2 $ and a horizontal line at $ f(x) = -2 $ for $ x > 2 $.
- Solid and open dots are swapped, which does not match the conditions given.

3. **Option C:**
- This graph illustrates a line where $ f(x) = -2 $ over all $ x $, which does not match the piecewise function.

4. **Option D:**
- This graph demonstrates a line where $ f(x) = -1 $ for all $ x $, not accurately representing the piecewise nature of the function.

### Solution Explanation:

The correct graph needs to reflect two segments;
- A horizontal line segment at $ f(x) = -2 $ extending up to and including $ x = 2 $.
- Another horizontal line segment at $ f(x) = -1 $ starting just after $ x = 2 $.

Thus:
- The correct graph is **Option A**.
- This graph correctly shows:
- A solid dot at (2, -2), indicating the function's value is -2 at $ x = 2 $.
- An open dot at (2, -1), indicating the function's value immediately changes to -1 for $ x > 2 $.

This detailed explanation should help you understand how to graph piecewise functions and identify the correct

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