### Piecewise Defined Function GraphThe image provided includes graphs for the piecewise defined function:\[ f(x) =\begin{cases} 0 & \text{if } x < 7 \\1 & \text{if } x \geq 7 \end{cases}\]#### Analysis of the Provided GraphsHere is a detailed explanation of each graph in the image:1. **Top Left Graph**: - **X-axis**: -10 to 10. - **Y-axis**: -10 to 10. - **Behavior**: - For $ x < 7 $, the function value is 0 (illustrated by the horizontal line at $ y = 0 $ extending from $-10$ to just before 7 on the x-axis with an open circle at $ x = 7 $). - For $ x \geq 7 $, the function value is 1 (represented by a horizontal line at $ y = 1 $ starting at $ x = 7 $ and moving to the right, with a solid circle at $ x = 7 $ indicating inclusion).2. **Top Right Graph**: - **X-axis**: -10 to 10. - **Y-axis**: -10 to 10. - **Behavior**: - For $ x < 7 $, the function value remains at 0 (horizontal line at $ y = 0 $). - For $ x \geq 7 $, the function value is 1. This is consistent with the definition, where at $ x = 7 $, the solid circle indicates $ f(7) = 1 $.3. **Bottom Left Graph**: - **X-axis**: -10 to 10. - **Y-axis**: -10 to 10. - **Behavior**: - For $ x < 7 $, the function value is 0. - For $ x \geq 7 $, the function value is 1 (solid circle at $ x = 7 $).4. **Bottom Right Graph**: - **X-axis**: -10 to 10. - **Y-axis**: -10 to 10. - **Behavior**: - This replicates the previous graphs:

Answered: Image /qna-images/answer/7876c5ef-3e08-4500-84b8-61b23e5288d1.jpg

Answered: Sketch a graph of the piecewise defined…

Sketch a graph of the piecewise defined function. if x < 7 1 if x 2 7 f(x) = y 10 10 - 10 10 -10 -5 10 -5 -10f -10아 y 10 10 -10 -5 5. 10 -10 -5 10 -5 -10 -10

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

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.

Question

### Piecewise Defined Function Graph

The image provided includes graphs for the piecewise defined function:

\[ f(x) =
\begin{cases}
0 & \text{if } x < 7 \\
1 & \text{if } x \geq 7
\end{cases}
\]

#### Analysis of the Provided Graphs

Here is a detailed explanation of each graph in the image:

1. **Top Left Graph**:
- **X-axis**: -10 to 10.
- **Y-axis**: -10 to 10.
- **Behavior**:
- For $ x < 7 $, the function value is 0 (illustrated by the horizontal line at $ y = 0 $ extending from $-10$ to just before 7 on the x-axis with an open circle at $ x = 7 $).
- For $ x \geq 7 $, the function value is 1 (represented by a horizontal line at $ y = 1 $ starting at $ x = 7 $ and moving to the right, with a solid circle at $ x = 7 $ indicating inclusion).

2. **Top Right Graph**:
- **X-axis**: -10 to 10.
- **Y-axis**: -10 to 10.
- **Behavior**:
- For $ x < 7 $, the function value remains at 0 (horizontal line at $ y = 0 $).
- For $ x \geq 7 $, the function value is 1. This is consistent with the definition, where at $ x = 7 $, the solid circle indicates $ f(7) = 1 $.

3. **Bottom Left Graph**:
- **X-axis**: -10 to 10.
- **Y-axis**: -10 to 10.
- **Behavior**:
- For $ x < 7 $, the function value is 0.
- For $ x \geq 7 $, the function value is 1 (solid circle at $ x = 7 $).

4. **Bottom Right Graph**:
- **X-axis**: -10 to 10.
- **Y-axis**: -10 to 10.
- **Behavior**:
- This replicates the previous graphs:

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