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Put the transformations that turn the graph of f (z) = 3 to the graph of f (x) = -3z+2 +4 %3D First 1 Shift left 2 units ! Shift up 4 units 3 Reflect horizontally across the y-axis Reflect vertically across the z-axis Last 2.

Put the transformations that turn the graph of f (z) = 3 to the graph of f (x) = -3z+2 +4 %3D First 1 Shift left 2 units ! Shift up 4 units 3 Reflect horizontally across the y-axis Reflect vertically across the z-axis Last 2.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Transformation of Graphs** To convert the graph of \( f(x) = 3^x \) to the graph of \( f(x) = -3^{-x+2} + 4 \), apply the following transformations in order: 1. **Shift left 2 units**: This operation moves the entire graph horizontally to the left by two units. 2. **Shift up 4 units**: This transformation raises the graph vertically upwards by four units. 3. **Reflect horizontally across the \( y \)-axis**: Reflect the graph over the \( y \)-axis, which inverts it horizontally. 4. **Reflect vertically across the \( x \)-axis**: Reflect the graph over the \( x \)-axis, flipping it vertically. Each transformation alters the position or orientation of the graph based on the modifications made to the function's equation.
Transcribed Image Text:**Transformation of Graphs** To convert the graph of \( f(x) = 3^x \) to the graph of \( f(x) = -3^{-x+2} + 4 \), apply the following transformations in order: 1. **Shift left 2 units**: This operation moves the entire graph horizontally to the left by two units. 2. **Shift up 4 units**: This transformation raises the graph vertically upwards by four units. 3. **Reflect horizontally across the \( y \)-axis**: Reflect the graph over the \( y \)-axis, which inverts it horizontally. 4. **Reflect vertically across the \( x \)-axis**: Reflect the graph over the \( x \)-axis, flipping it vertically. Each transformation alters the position or orientation of the graph based on the modifications made to the function's equation.
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