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
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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![### 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 \( f \).
\[ g(x) = -4 \cdot ( f(x) ) + 1 \]
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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 \( f \).
\[ g(x) = -4 \cdot ( f(x) ) + 1 \]
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