Determine the cubic function that is obtained from the parent function y =x3 under a vertical stretch by a factor of 2, a reflection across the x-axis, a vertical translation 5 units up, and a horizontal translation 4 uni Choose the correct answer below. O A. y= - 2(x +5)3 + 4 O B. y= -(x+5)3 +4 OC. y= 2(x-4)3 -5 O D. y= - +5 O E. y= -2(x + 4)3 + 5

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
icon
Related questions
icon
Concept explainers
Topic Video
Question

My question is in the picture.

### Determining the Modified Cubic Function

**Problem Statement:**
Determine the cubic function that is obtained from the parent function \( y = x^3 \) under the following transformations:
1. A vertical stretch by a factor of 2,
2. A reflection across the x-axis,
3. A vertical translation 5 units up,
4. A horizontal translation 4 units left.

**Choose the correct answer below:**
- **A.** \( y = -2(x + 5)^3 + 4 \)
- **B.** \( y = -\frac{1}{2}(x + 5)^3 + 4 \)
- **C.** \( y = 2(x - 4)^3 - 5 \)
- **D.** \( y = -\frac{1}{2}(x + 4)^3 + 5 \)
- **E.** \( y = -2(x + 4)^3 + 5 \)
- **F.** \( y = 2(x + 5)^3 + 4 \)

**Explanation of the Correct Answer:**

1. **Horizontal Translation 4 Units Left:** 
   - To translate the function \( 4 \) units to the left, we replace \( x \) with \( (x + 4) \). 
   - The function becomes \( y = (x + 4)^3 \).

2. **Vertical Stretch by a Factor of 2:**
   - A vertical stretch by a factor of \( 2 \) involves multiplying the function by \( 2 \).
   - The function now is \( y = 2(x + 4)^3 \).

3. **Reflection Across the X-axis:**
   - Reflecting the function across the x-axis involves multiplying by \( -1 \).
   - The function becomes \( y = -2(x + 4)^3 \).

4. **Vertical Translation 5 Units Up:**
   - To translate the function \( 5 \) units up, we add \( 5 \) to the function.
   - The function finally becomes \( y = -2(x + 4)^3 + 5 \).

**Answer:**

- **Option E:** \( y = -2(x + 4)^3 + 5 \) is correct.

This explanation breaks down each transformation step-by-step, helping students to understand how the final function
Transcribed Image Text:### Determining the Modified Cubic Function **Problem Statement:** Determine the cubic function that is obtained from the parent function \( y = x^3 \) under the following transformations: 1. A vertical stretch by a factor of 2, 2. A reflection across the x-axis, 3. A vertical translation 5 units up, 4. A horizontal translation 4 units left. **Choose the correct answer below:** - **A.** \( y = -2(x + 5)^3 + 4 \) - **B.** \( y = -\frac{1}{2}(x + 5)^3 + 4 \) - **C.** \( y = 2(x - 4)^3 - 5 \) - **D.** \( y = -\frac{1}{2}(x + 4)^3 + 5 \) - **E.** \( y = -2(x + 4)^3 + 5 \) - **F.** \( y = 2(x + 5)^3 + 4 \) **Explanation of the Correct Answer:** 1. **Horizontal Translation 4 Units Left:** - To translate the function \( 4 \) units to the left, we replace \( x \) with \( (x + 4) \). - The function becomes \( y = (x + 4)^3 \). 2. **Vertical Stretch by a Factor of 2:** - A vertical stretch by a factor of \( 2 \) involves multiplying the function by \( 2 \). - The function now is \( y = 2(x + 4)^3 \). 3. **Reflection Across the X-axis:** - Reflecting the function across the x-axis involves multiplying by \( -1 \). - The function becomes \( y = -2(x + 4)^3 \). 4. **Vertical Translation 5 Units Up:** - To translate the function \( 5 \) units up, we add \( 5 \) to the function. - The function finally becomes \( y = -2(x + 4)^3 + 5 \). **Answer:** - **Option E:** \( y = -2(x + 4)^3 + 5 \) is correct. This explanation breaks down each transformation step-by-step, helping students to understand how the final function
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Sample space, Events, and Basic Rules of Probability
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education