29. y = x- 2 33. y (x- 3) + 2 30. y x + 3 34. y (x + 2)² + 1 32. y (x- 2) 36. y = -(x + 2) 31. y = (x + 1) 35. y = -(1- x)²

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
icon
Concept explainers
Topic Video
Question

Please only answer the questions marked in red. Thank you!

### Graphing Functions with Transformations

This section focuses on how to graph functions using various transformations. The primary graphs provided illustrate transformations pertaining to a parent function \( f(x) \) and another function \( g(x) \). These visual aids will help in understanding how transformations such as shifts, reflections, stretches, and compressions affect the graph of a function.

#### Problems and Graphs:

1. **Exercise 21 to 28**: The first set of problems (21-28) involves transformations of the function \( f(x) \) and \( g(x) \). The transformations include horizontal and vertical shifts, reflections, and dilations. Let's review explicit examples and their corresponding general transformations:

    - **Exercise 21**: \( y = f(x - 2) - 3 \)
        - **Transformation**: Shift right by 2 units and down by 3 units.
    - **Exercise 22**: \( y = f(x + 1) - 2 \)
        - **Transformation**: Shift left by 1 unit and down by 2 units.
    - **Exercise 23**: \( y = -f(x - 1) + 2 \)
        - **Transformation**: Reflect across the x-axis, shift right by 1 unit, and up by 2 units.
    - **Exercise 24**: \( y = -2f(x) + 1 \)
        - **Transformation**: Reflect across the x-axis, vertical stretch by a factor of 2, and shift up by 1 unit.
    - **Exercise 25**: \( y = -\frac{1}{2}g(x) \)
        - **Transformation**: Reflect across the x-axis and vertical compression by a factor of 1/2.
    - **Exercise 26**: \( y =  \frac{1}{4}g(-x) \)
        - **Transformation**: Reflect across the y-axis and vertical compression by a factor of 1/4.
    - **Exercise 27**: \( y = -g(2x) \)
        - **Transformation**: Reflect across the x-axis and horizontal compression by a factor of 1/2.
    - **Exercise 28**: \( y = g\left( \frac{1}{2}x \right) \)
        - **Transformation**: Horizontal stretch by a factor of
Transcribed Image Text:### Graphing Functions with Transformations This section focuses on how to graph functions using various transformations. The primary graphs provided illustrate transformations pertaining to a parent function \( f(x) \) and another function \( g(x) \). These visual aids will help in understanding how transformations such as shifts, reflections, stretches, and compressions affect the graph of a function. #### Problems and Graphs: 1. **Exercise 21 to 28**: The first set of problems (21-28) involves transformations of the function \( f(x) \) and \( g(x) \). The transformations include horizontal and vertical shifts, reflections, and dilations. Let's review explicit examples and their corresponding general transformations: - **Exercise 21**: \( y = f(x - 2) - 3 \) - **Transformation**: Shift right by 2 units and down by 3 units. - **Exercise 22**: \( y = f(x + 1) - 2 \) - **Transformation**: Shift left by 1 unit and down by 2 units. - **Exercise 23**: \( y = -f(x - 1) + 2 \) - **Transformation**: Reflect across the x-axis, shift right by 1 unit, and up by 2 units. - **Exercise 24**: \( y = -2f(x) + 1 \) - **Transformation**: Reflect across the x-axis, vertical stretch by a factor of 2, and shift up by 1 unit. - **Exercise 25**: \( y = -\frac{1}{2}g(x) \) - **Transformation**: Reflect across the x-axis and vertical compression by a factor of 1/2. - **Exercise 26**: \( y = \frac{1}{4}g(-x) \) - **Transformation**: Reflect across the y-axis and vertical compression by a factor of 1/4. - **Exercise 27**: \( y = -g(2x) \) - **Transformation**: Reflect across the x-axis and horizontal compression by a factor of 1/2. - **Exercise 28**: \( y = g\left( \frac{1}{2}x \right) \) - **Transformation**: Horizontal stretch by a factor of
Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

Blurred answer
Knowledge Booster
Centre, Spread, and Shape of a Distribution
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,