Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![### Graphing Functions
#### Instructions:
Draw the graph of the function \( f(x) = 13\sqrt{-x-2} + 2 \) using the coordinate grid provided below.
#### Coordinate Grid:
- The coordinate grid ranges from -8 to 8 on both the x-axis and y-axis.
- The origin (0,0) is located at the center of the grid.
- Each unit on the grid is marked with a fine line.
#### Tools Provided:
Below the grid, there are several tools to aid in drawing the graph:
1. **Clear All**: Resets the graph to its blank state.
2. **Draw**: A selectable tool that allows for drawing different types of curves and shapes on the grid. The options include:
- A straight line
- A standard parabolic curve (both up and down)
- A simple curve
- A circle
#### Drawing the Function:
To graph the function \( f(x) = 13\sqrt{-x-2} + 2 \):
1. **Identify Points**: Determine key points by substituting various values of \( x \) into the function to find corresponding \( y \)-values. This is particularly important as it helps in understanding the behavior of the graph.
2. **Plot Key Points**: Mark the computed points on the graph.
3. **Draw the Curve**: Use the provided drawing tools to connect the points smoothly, following the expected shape of the graph.
*Ensure accuracy and neatness while plotting and drawing to reflect the true nature of the function.*
### Example Calculation:
For \( x = -2 \):
\[ f(-2) = 13\sqrt{-(-2)-2} + 2 = 13\sqrt{0} + 2 = 2 \]
Thus, one key point is (-2, 2). Continue calculating and plotting for various \( x \)-values to complete the graph.
### Note:
This function involves a square root, and the domain of the function is restricted such that the expression inside the square root must be non-negative. Thus, the graph will only exist for values of \( x \) that satisfy \( -x-2 \geq 0 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8aee7c7d-285e-49c9-ad3b-faae5963cfad%2F2dc5618a-984f-4859-bb29-f329bb62bd44%2Fn38hhmo_processed.png&w=3840&q=75)
Transcribed Image Text:### Graphing Functions
#### Instructions:
Draw the graph of the function \( f(x) = 13\sqrt{-x-2} + 2 \) using the coordinate grid provided below.
#### Coordinate Grid:
- The coordinate grid ranges from -8 to 8 on both the x-axis and y-axis.
- The origin (0,0) is located at the center of the grid.
- Each unit on the grid is marked with a fine line.
#### Tools Provided:
Below the grid, there are several tools to aid in drawing the graph:
1. **Clear All**: Resets the graph to its blank state.
2. **Draw**: A selectable tool that allows for drawing different types of curves and shapes on the grid. The options include:
- A straight line
- A standard parabolic curve (both up and down)
- A simple curve
- A circle
#### Drawing the Function:
To graph the function \( f(x) = 13\sqrt{-x-2} + 2 \):
1. **Identify Points**: Determine key points by substituting various values of \( x \) into the function to find corresponding \( y \)-values. This is particularly important as it helps in understanding the behavior of the graph.
2. **Plot Key Points**: Mark the computed points on the graph.
3. **Draw the Curve**: Use the provided drawing tools to connect the points smoothly, following the expected shape of the graph.
*Ensure accuracy and neatness while plotting and drawing to reflect the true nature of the function.*
### Example Calculation:
For \( x = -2 \):
\[ f(-2) = 13\sqrt{-(-2)-2} + 2 = 13\sqrt{0} + 2 = 2 \]
Thus, one key point is (-2, 2). Continue calculating and plotting for various \( x \)-values to complete the graph.
### Note:
This function involves a square root, and the domain of the function is restricted such that the expression inside the square root must be non-negative. Thus, the graph will only exist for values of \( x \) that satisfy \( -x-2 \geq 0 \).
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