Problem attached- Graph each pair on same plane using transformations. please label each function on the graph. Do not make a table of values. ### Graphing Transformations of Polynomial FunctionsIn this exercise, we aim to graph the pair of functions \( f(x) = x^3 \) and \( g(x) = (x + 5)^3 \) on the same coordinate plane using transformations. We will not make a table of values but will label each function on the graph. #### Functions to be Graphed:1. \( f(x) = x^3 \)2. \( g(x) = (x + 5)^3 \)#### Description of the Coordinate Plane:A coordinate plane is provided with the x-axis and y-axis both ranging from -10 to 10. Each axis is labeled and marked with increments of 1 unit.### Transformations:The function \( f(x) = x^3 \) is the standard cubic function which passes through the origin (0,0) and has an 'S' shape. The function \( g(x) = (x + 5)^3 \) is a transformation of the standard cubic function. In this case, \( g(x) \) is \( f(x) \) shifted 5 units to the left.#### Explanation of the Graphs:- The parent cubic function \( f(x) = x^3 \): - It passes through the origin. - Characteristics points include (0,0), (1,1), (-1,-1), (2,8), and (-2,-8). - The graph has a point of inflection at the origin where the slope changes.- The transformed function \( g(x) = (x + 5)^3 \): - Derived by shifting the parent function \( x^3 \) 5 units to the left. - The inflection point of \( g(x) \) is at (-5,0). - It follows the same 'S' shape as \( f(x) = x^3 \), just translated.### Instruction:Label each function on the graph. Ensure \( f(x) \) is correctly represented by a bold or distinct line to differentiate it from \( g(x) \).By graphing these functions, we understand how the transformation (horizontal shift in this case) affects the graph of the parent function.

Answered: Graph the pair of functions on the same…

Graph the pair of functions on the same plane using transformations. Do not make a table of values. Label each function on the graph. f(x) = x3, g(x) = (x + 5)3 10+ -10 -5 -10- 5 10 X

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

Problem attached- Graph each pair on same plane using transformations. please label each function on the graph. Do not make a table of values.

### Graphing Transformations of Polynomial Functions

In this exercise, we aim to graph the pair of functions \( f(x) = x^3 \) and \( g(x) = (x + 5)^3 \) on the same coordinate plane using transformations. We will not make a table of values but will label each function on the graph.

#### Functions to be Graphed:
1. \( f(x) = x^3 \)
2. \( g(x) = (x + 5)^3 \)

#### Description of the Coordinate Plane:

A coordinate plane is provided with the x-axis and y-axis both ranging from -10 to 10. Each axis is labeled and marked with increments of 1 unit.

### Transformations:
The function \( f(x) = x^3 \) is the standard cubic function which passes through the origin (0,0) and has an 'S' shape.

The function \( g(x) = (x + 5)^3 \) is a transformation of the standard cubic function. In this case, \( g(x) \) is \( f(x) \) shifted 5 units to the left.

#### Explanation of the Graphs:

- The parent cubic function \( f(x) = x^3 \):
- It passes through the origin.
- Characteristics points include (0,0), (1,1), (-1,-1), (2,8), and (-2,-8).
- The graph has a point of inflection at the origin where the slope changes.

- The transformed function \( g(x) = (x + 5)^3 \):
- Derived by shifting the parent function \( x^3 \) 5 units to the left.
- The inflection point of \( g(x) \) is at (-5,0).
- It follows the same 'S' shape as \( f(x) = x^3 \), just translated.

### Instruction:
Label each function on the graph. Ensure \( f(x) \) is correctly represented by a bold or distinct line to differentiate it from \( g(x) \).

By graphing these functions, we understand how the transformation (horizontal shift in this case) affects the graph of the parent function.

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