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Parent Function f(x) = 2x+¹ Growth or Decay a = 1 b=2 X -1 0 1 y Transformation: -2 -17 16 15 14 13 12 11 10

Parent Function f(x) = 2x+¹ Growth or Decay a = 1 b=2 X -1 0 1 y Transformation: -2 -17 16 15 14 13 12 11 10

Algebra and Trigonometry (6th Edition)
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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### Exponential Functions and Transformations #### Parent Function **Function:** \( f(x) = 2^{x+1} \) **Characteristics:** - **Growth or Decay:** Growth - **Base:** \( b = 2 \) - **Coefficient of \( x \):** \( a = 1 \) #### Table of Values | x | y | |----|---------| | -1 | \( 2^x \) | | 0 | | | 1 | | #### Graph Explanation The graph is plotted on a standard Cartesian coordinate system. The x-axis and y-axis both range from -8 to 8. The exponential function \( f(x) = 2^{x+1} \) is expected to show exponential growth, with the curve rising steeply as \( x \) increases. #### Graph Structure - **X-Axis:** Range from -8 to 8 - **Y-Axis:** Range from 0 to 16 - **Transformation Section:** Space is provided to note any transformations made to the parent function’s graph. This visualization helps in understanding the behavior of exponential functions and how they react to transformations.
Transcribed Image Text:### Exponential Functions and Transformations #### Parent Function **Function:** \( f(x) = 2^{x+1} \) **Characteristics:** - **Growth or Decay:** Growth - **Base:** \( b = 2 \) - **Coefficient of \( x \):** \( a = 1 \) #### Table of Values | x | y | |----|---------| | -1 | \( 2^x \) | | 0 | | | 1 | | #### Graph Explanation The graph is plotted on a standard Cartesian coordinate system. The x-axis and y-axis both range from -8 to 8. The exponential function \( f(x) = 2^{x+1} \) is expected to show exponential growth, with the curve rising steeply as \( x \) increases. #### Graph Structure - **X-Axis:** Range from -8 to 8 - **Y-Axis:** Range from 0 to 16 - **Transformation Section:** Space is provided to note any transformations made to the parent function’s graph. This visualization helps in understanding the behavior of exponential functions and how they react to transformations.
**Algebra 2 Worksheet** --- **Name:** **Date:** **Period:** --- **Parent Function** \[ f(x) = 2^{x-1} \] - **Growth or Decay** - \( a = \) - \( b = \) | \( x \) | \( y \) | |----------|----------| | -1 | | | 0 | | | 1 | | **Transformation:** --- **Graph Description:** The worksheet includes a coordinate grid for plotting the function. The grid has labeled axes, ranging from -18 to 18 on both the x and y axes, with additional grid lines indicating increments for more precise plotting. There is space for students to plot points corresponding to the function \( f(x) = 2^{x-1} \) and its transformations.
Transcribed Image Text:**Algebra 2 Worksheet** --- **Name:** **Date:** **Period:** --- **Parent Function** \[ f(x) = 2^{x-1} \] - **Growth or Decay** - \( a = \) - \( b = \) | \( x \) | \( y \) | |----------|----------| | -1 | | | 0 | | | 1 | | **Transformation:** --- **Graph Description:** The worksheet includes a coordinate grid for plotting the function. The grid has labeled axes, ranging from -18 to 18 on both the x and y axes, with additional grid lines indicating increments for more precise plotting. There is space for students to plot points corresponding to the function \( f(x) = 2^{x-1} \) and its transformations.
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