Review later 7. Explain the difference in the movement of the parent function, f(x), given the constraint that k is a positive value. s(z) : f(2) + k g(z) = f(z+k) %3D %3D

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section: Chapter Questions
Problem 74SGR
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**Understanding Transformations of Functions**

**7. Explain the difference in the movement of the parent function, \( f(x) \), given the constraint that \( k \) is a positive value.**

### Horizontal and Vertical Shifts:

- **Vertical Shift**: 
  The function \( g(x) = f(x) + k \) represents a vertical shift of the parent function \( f(x) \). If \( k \) is positive, the graph of \( f(x) \) is shifted **upwards** by \( k \) units.

- **Horizontal Shift**: 
  The function \( g(x) = f(x + k) \) represents a horizontal shift of the parent function \( f(x) \). If \( k \) is positive, the graph of \( f(x) \) is shifted **left** by \( k \) units.

This fundamental concept in algebra and calculus is crucial for understanding how different transformations affect the graph of a function. Analyzing these shifts helps in graph sketching and in solving equations involving transformed functions.

### Interface Overview

The provided image also showcases a typical text editor interface within an educational platform. Key features include text formatting options like bold, italic, underline, and special characters, aiding in the clear and structured presentation of mathematical concepts.
Transcribed Image Text:**Understanding Transformations of Functions** **7. Explain the difference in the movement of the parent function, \( f(x) \), given the constraint that \( k \) is a positive value.** ### Horizontal and Vertical Shifts: - **Vertical Shift**: The function \( g(x) = f(x) + k \) represents a vertical shift of the parent function \( f(x) \). If \( k \) is positive, the graph of \( f(x) \) is shifted **upwards** by \( k \) units. - **Horizontal Shift**: The function \( g(x) = f(x + k) \) represents a horizontal shift of the parent function \( f(x) \). If \( k \) is positive, the graph of \( f(x) \) is shifted **left** by \( k \) units. This fundamental concept in algebra and calculus is crucial for understanding how different transformations affect the graph of a function. Analyzing these shifts helps in graph sketching and in solving equations involving transformed functions. ### Interface Overview The provided image also showcases a typical text editor interface within an educational platform. Key features include text formatting options like bold, italic, underline, and special characters, aiding in the clear and structured presentation of mathematical concepts.
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