Sketch the graphs of the following using transformations 19) peints): siq naviy od doen g(x) = -√√x +3 A-(0)1(T
Sketch the graphs of the following using transformations 19) peints): siq naviy od doen g(x) = -√√x +3 A-(0)1(T
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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Question
![**Sketch the Graphs Using Transformations**
Use the following transformation to sketch the graph:
\[ g(x) = -\sqrt{x} + 3 \]
**Graph Description:**
The graph is initially a blank coordinate grid with equal spacing, featuring horizontal and vertical axes. This grid will be used to plot the function by applying the given transformation.
- **Transformation Steps**:
- **Reflection**: The graph of \( \sqrt{x} \) is reflected across the x-axis due to the negative sign, resulting in a downward-opening curve.
- **Vertical Shift**: The entire graph of the function \( -\sqrt{x} \) is shifted 3 units upward, modifying the range of the function accordingly.
**Key Points to Plot**:
1. Starting with the basic shape of \( \sqrt{x} \) which is reflected downwards.
2. Adjusting for the vertical shift by raising the curve up 3 units on the y-axis.
This depiction aids in understanding how transformations affect the sketch of a function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b3e2b09-123d-4bda-aba2-2450a44862a9%2F6b93341f-007f-4335-9388-805ca61dfd09%2Ftsy5v3a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Sketch the Graphs Using Transformations**
Use the following transformation to sketch the graph:
\[ g(x) = -\sqrt{x} + 3 \]
**Graph Description:**
The graph is initially a blank coordinate grid with equal spacing, featuring horizontal and vertical axes. This grid will be used to plot the function by applying the given transformation.
- **Transformation Steps**:
- **Reflection**: The graph of \( \sqrt{x} \) is reflected across the x-axis due to the negative sign, resulting in a downward-opening curve.
- **Vertical Shift**: The entire graph of the function \( -\sqrt{x} \) is shifted 3 units upward, modifying the range of the function accordingly.
**Key Points to Plot**:
1. Starting with the basic shape of \( \sqrt{x} \) which is reflected downwards.
2. Adjusting for the vertical shift by raising the curve up 3 units on the y-axis.
This depiction aids in understanding how transformations affect the sketch of a function.
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