I am having a hard time solving these problems for my homework. **Title: Understanding Function Transformations****Description:**This tutorial aims to help you understand how a given function can be derived from basic function transformations and graph it accordingly.**Task:**Given the function $ g(x) = - (x + 7)^3 $:1. Describe how this function can be obtained from one of the basic graphs.2. Graph the function based on the given transformations.**Instructions:**Select the correct choice below and fill in the answer box to complete your choice.**Options:**- **A.** Start with the graph of $ f(x) = \boxed{\quad} $. Shift it right 7 units and then reflect it across the x-axis.- **B.** Start with the graph of $ f(x) = \boxed{\quad} $. Shift it left 7 units and then reflect it across the y-axis.- **C.** Start with the graph of $ f(x) = \boxed{\quad} $. Shift it left 7 units and then reflect it across the x-axis.- **D.** Start with the graph of $ f(x) = \boxed{\quad} $. Shift it right 7 units and then reflect it across the y-axis.**Explanation:**- **Choices A and D:** Both discuss shifting the graph right 7 units.- **Choices B and C:** Both discuss shifting the graph left 7 units.Depending on the chosen shifts and reflections, you need to determine the correct initial function $ f(x) $ and how to apply the transformations. Understanding function transformations is crucial for analyzing and graphing different polynomial forms and understanding shifts and reflections related to the basic form of the graph.**Additional Tips:**When you shift a function:- Shifting right involves $ (x - h) $- Shifting left involves $ (x + h) $When reflecting a function:- Across the x-axis involves multiplying the outside of the function by -1 (i.e., $ -f(x) $)- Across the y-axis involves reflecting the $ x $ term inside the function (i.e., $ f(-x) $)Apply these transformations sequentially to understand how the given function $ g(x) = - (x + 7)^3 $ is derived.

The given function .We have to describe the transformation of the function.

Answered: Describe how the given function can be…

Math

Algebra

Describe how the given function can be obtained from one of the basic graphs. Then graph the function. g(x) = -(x+7)³

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,...

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Question

I am having a hard time solving these problems for my homework.

**Title: Understanding Function Transformations**

**Description:**
This tutorial aims to help you understand how a given function can be derived from basic function transformations and graph it accordingly.

**Task:**
Given the function $ g(x) = - (x + 7)^3 $:

1. Describe how this function can be obtained from one of the basic graphs.
2. Graph the function based on the given transformations.

**Instructions:**

Select the correct choice below and fill in the answer box to complete your choice.

**Options:**

- **A.** Start with the graph of $ f(x) = \boxed{\quad} $. Shift it right 7 units and then reflect it across the x-axis.

- **B.** Start with the graph of $ f(x) = \boxed{\quad} $. Shift it left 7 units and then reflect it across the y-axis.

- **C.** Start with the graph of $ f(x) = \boxed{\quad} $. Shift it left 7 units and then reflect it across the x-axis.

- **D.** Start with the graph of $ f(x) = \boxed{\quad} $. Shift it right 7 units and then reflect it across the y-axis.

**Explanation:**

- **Choices A and D:** Both discuss shifting the graph right 7 units.
- **Choices B and C:** Both discuss shifting the graph left 7 units.

Depending on the chosen shifts and reflections, you need to determine the correct initial function $ f(x) $ and how to apply the transformations.

Understanding function transformations is crucial for analyzing and graphing different polynomial forms and understanding shifts and reflections related to the basic form of the graph.

**Additional Tips:**

When you shift a function:
- Shifting right involves $ (x - h) $
- Shifting left involves $ (x + h) $

When reflecting a function:
- Across the x-axis involves multiplying the outside of the function by -1 (i.e., $ -f(x) $)
- Across the y-axis involves reflecting the $ x $ term inside the function (i.e., $ f(-x) $)

Apply these transformations sequentially to understand how the given function $ g(x) = - (x + 7)^3 $ is derived.

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