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Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Question
![### Understanding Graph Functions
#### Problem Statement
A function \( f \) is given:
\[ f(x) = 8 - 2x, \quad 1 < x < 3 \]
##### (a) Graph the Function \( f \)
You are asked to sketch a graph of the function \( f \).
##### Graphing Interface Description
You are provided with a graphing tool from WebAssign. The graph has the following features:
- **Toolbar**: Located on the left side of the graph, this allows you to select tools like the pen for drawing, a tool for adding points, line tools, shape tools like a circle, and a fill tool.
- **Graph Layer Options**: On the right-hand side, there are options to manage graph layers where you can add and adjust layers and their properties.
- **Graph**: The graph is a standard Cartesian coordinate system with both the x- and y-axes ranging from -10 to 10. The gridlines are marked and numbered.
##### Instructions for Graphing
1. Use the graphing tools to plot the line representing \( f(x) = 8 - 2x \).
2. Ensure you limit the drawing to the interval \( 1 < x < 3 \).
##### (b) Determine Domain and Range
Use the graph to determine the domain and range of \( f \). Enter your answers using interval notation.
###### Domain
Fill in the appropriate values for the domain.
###### Range
Fill in the appropriate values for the range.
---
### Solution Guide
To solve part (a), use the equation \( f(x) = 8 - 2x \) for \( 1 < x < 3 \) and plot the respective points on the graph.
For part (b), analyze the graph you've drawn to find the following:
- **Domain**: The set of all x-values within the interval \( 1 < x < 3 \).
- **Range**: The corresponding y-values for the x-values within the domain.
#### Useful Tips:
- For the line \( f(x) = 8 - 2x \):
- When \( x = 1 \), \( f(x) = 6 \)
- When \( x = 3 \), \( f(x) = 2 \)
- Since \( x \) is between 1 and 3, exclusive, the points on the graph should reflect this interval.](https://content.bartleby.com/qna-images/question/cf307311-1e00-4fe9-8eeb-e087e581a37a/a5934a2c-e442-484d-a5dc-227257790a26/y8ajf6w_thumbnail.png)
Transcribed Image Text:### Understanding Graph Functions
#### Problem Statement
A function \( f \) is given:
\[ f(x) = 8 - 2x, \quad 1 < x < 3 \]
##### (a) Graph the Function \( f \)
You are asked to sketch a graph of the function \( f \).
##### Graphing Interface Description
You are provided with a graphing tool from WebAssign. The graph has the following features:
- **Toolbar**: Located on the left side of the graph, this allows you to select tools like the pen for drawing, a tool for adding points, line tools, shape tools like a circle, and a fill tool.
- **Graph Layer Options**: On the right-hand side, there are options to manage graph layers where you can add and adjust layers and their properties.
- **Graph**: The graph is a standard Cartesian coordinate system with both the x- and y-axes ranging from -10 to 10. The gridlines are marked and numbered.
##### Instructions for Graphing
1. Use the graphing tools to plot the line representing \( f(x) = 8 - 2x \).
2. Ensure you limit the drawing to the interval \( 1 < x < 3 \).
##### (b) Determine Domain and Range
Use the graph to determine the domain and range of \( f \). Enter your answers using interval notation.
###### Domain
Fill in the appropriate values for the domain.
###### Range
Fill in the appropriate values for the range.
---
### Solution Guide
To solve part (a), use the equation \( f(x) = 8 - 2x \) for \( 1 < x < 3 \) and plot the respective points on the graph.
For part (b), analyze the graph you've drawn to find the following:
- **Domain**: The set of all x-values within the interval \( 1 < x < 3 \).
- **Range**: The corresponding y-values for the x-values within the domain.
#### Useful Tips:
- For the line \( f(x) = 8 - 2x \):
- When \( x = 1 \), \( f(x) = 6 \)
- When \( x = 3 \), \( f(x) = 2 \)
- Since \( x \) is between 1 and 3, exclusive, the points on the graph should reflect this interval.
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