Home Browsing Sesh Lunch Education Gaming Guides The function g is related to one of the parent functions. 9(x) = -4x² + 1 (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (Select all that apply.) O reflection in the x-axis O vertical shift of 4 units upward horizontal shift of 1 unit to the right Overtical stretch Overtical shrink Overtical shift of 1 unit upward (c) Sketch the graph of g. -10 -10 -10 10 Tech related Online Shopping 19 10 10 X -10 -10 Work Search -5 10 WebAssign Plot 10 - 10/ Micrologic 10 10 Email and Work
Home Browsing Sesh Lunch Education Gaming Guides The function g is related to one of the parent functions. 9(x) = -4x² + 1 (a) Identify the parent function f. (b) Describe the sequence of transformations from f to g. (Select all that apply.) O reflection in the x-axis O vertical shift of 4 units upward horizontal shift of 1 unit to the right Overtical stretch Overtical shrink Overtical shift of 1 unit upward (c) Sketch the graph of g. -10 -10 -10 10 Tech related Online Shopping 19 10 10 X -10 -10 Work Search -5 10 WebAssign Plot 10 - 10/ Micrologic 10 10 Email and Work
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.7: A Library Of Parent Functions
Problem 47E
Related questions
Question
2.55
![### Transformation of Functions
The following section is related to one of the parent functions.
Given Function:
\[ g(x) = -4x^2 + 1 \]
#### (a) Identify the parent function \( f \).
**Parent Function:**
\[ f(x) = x^2 \]
#### (b) Describe the sequence of transformations from \( f \) to \( g \). (Select all that apply.)
- [ ] reflection in the x-axis
- [ ] vertical shift of 4 units upward
- [x] horizontal shift of 1 unit to the right
- [x] vertical stretch
- [x] vertical shrink
- [x] vertical shift of 1 unit upward
#### (c) Sketch the graph of \( g \).
##### Graph 1:
- **Axes:** The graph features an \( x \)-axis ranging from -10 to 10, and a \( y \)-axis ranging from -10 to 10.
- **Plot:** This is a downward-opening parabola passing through points (-5, -9) and (5, -9), indicating the transformation includes reflection across the x-axis, vertical stretching, and an upward shift.
##### Graph 2:
- **Axes:** The graph also features an \( x \)-axis ranging from -10 to 10, and a \( y \)-axis ranging from -10 to 10.
- **Plot:** This graph shows an upward-opening parabola passing through points (-5, 9) and (5, 9), indicating no reflection, just a vertical stretch and upward shift.
#### (d) Use function notation to write \( g \) in terms of \( f \).
\[ g(x) = -4 \cdot ( f(x) ) + 1 \]
**Need Help?** Contact support.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F86020f22-4efe-437b-8b05-308770976ff7%2Fb2f32b41-63e0-4215-b94a-c1d40f4441e5%2Ftbb8njl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Transformation of Functions
The following section is related to one of the parent functions.
Given Function:
\[ g(x) = -4x^2 + 1 \]
#### (a) Identify the parent function \( f \).
**Parent Function:**
\[ f(x) = x^2 \]
#### (b) Describe the sequence of transformations from \( f \) to \( g \). (Select all that apply.)
- [ ] reflection in the x-axis
- [ ] vertical shift of 4 units upward
- [x] horizontal shift of 1 unit to the right
- [x] vertical stretch
- [x] vertical shrink
- [x] vertical shift of 1 unit upward
#### (c) Sketch the graph of \( g \).
##### Graph 1:
- **Axes:** The graph features an \( x \)-axis ranging from -10 to 10, and a \( y \)-axis ranging from -10 to 10.
- **Plot:** This is a downward-opening parabola passing through points (-5, -9) and (5, -9), indicating the transformation includes reflection across the x-axis, vertical stretching, and an upward shift.
##### Graph 2:
- **Axes:** The graph also features an \( x \)-axis ranging from -10 to 10, and a \( y \)-axis ranging from -10 to 10.
- **Plot:** This graph shows an upward-opening parabola passing through points (-5, 9) and (5, 9), indicating no reflection, just a vertical stretch and upward shift.
#### (d) Use function notation to write \( g \) in terms of \( f \).
\[ g(x) = -4 \cdot ( f(x) ) + 1 \]
**Need Help?** Contact support.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:
9781337278461
Author:
Ron Larson
Publisher:
Cengage Learning
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
