Describe how the graph of the following function can be obtained from one of the basic graphs. 1 g(x) = -(x + 2)² Start with the graph of y= Shift it unit(s), ▼it ... by multiplying each by and then reflect it across the
Describe how the graph of the following function can be obtained from one of the basic graphs. 1 g(x) = -(x + 2)² Start with the graph of y= Shift it unit(s), ▼it ... by multiplying each by and then reflect it across the
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![## Description of the Graph Transformation
The task is to describe how the graph of the given function can be obtained from one of the basic graphs.
### Function:
\[
g(x) = -\frac{1}{3}(x+2)^2
\]
### Steps to Graph the Function:
1. **Start with the graph of:** (Select the appropriate basic function from options, such as \( y = x^2 \)).
2. **Shift it:** (Choose between left or right and specify the number of units).
3. **Units:** (Specify the number of units the graph is shifted).
4. **By multiplying each by:** (Specify the factor to multiply; in this case, by -1/3).
5. **Reflect it across the:** (Select the axis of reflection, such as x-axis or y-axis).
### Graphical Explanation:
- **Basic Graph:** Begin with the graph of a basic quadratic function, typically \( y = x^2 \).
- **Horizontal Shift:** Adjust the graph horizontally according to \( (x+2)^2 \), indicating a shift 2 units to the left.
- **Vertical Stretch/Compression and Reflection:** Multiply by \(-\frac{1}{3}\) to compress vertically and reflect it across the x-axis, indicating a downward opening.
This step-by-step process helps in visualizing how transformations affect the graph of the quadratic function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f78fe67-9f65-4591-abf6-cb97fc8e35e5%2F9aa7286f-a7ea-44f8-bbe7-6b9f5feaadfa%2Fpp1khva_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Description of the Graph Transformation
The task is to describe how the graph of the given function can be obtained from one of the basic graphs.
### Function:
\[
g(x) = -\frac{1}{3}(x+2)^2
\]
### Steps to Graph the Function:
1. **Start with the graph of:** (Select the appropriate basic function from options, such as \( y = x^2 \)).
2. **Shift it:** (Choose between left or right and specify the number of units).
3. **Units:** (Specify the number of units the graph is shifted).
4. **By multiplying each by:** (Specify the factor to multiply; in this case, by -1/3).
5. **Reflect it across the:** (Select the axis of reflection, such as x-axis or y-axis).
### Graphical Explanation:
- **Basic Graph:** Begin with the graph of a basic quadratic function, typically \( y = x^2 \).
- **Horizontal Shift:** Adjust the graph horizontally according to \( (x+2)^2 \), indicating a shift 2 units to the left.
- **Vertical Stretch/Compression and Reflection:** Multiply by \(-\frac{1}{3}\) to compress vertically and reflect it across the x-axis, indicating a downward opening.
This step-by-step process helps in visualizing how transformations affect the graph of the quadratic function.
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