
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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Problem attached- Graph each pair on same plane using transformations. please label each function on the graph. Do not make a table of values.

Transcribed Image Text:### 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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