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Determine the graph for each g (x) function if the parent function is f(x) = x. Graph both functions on the same coordinate plane. 1) g(x)=f(x)+4 3) g(x)= -f(x) 30 2) g(x)=√(x) -10 -8. Praes +8 10 -30 4) g(x)=3√(x) 10 5 Paus 10

Determine the graph for each g (x) function if the parent function is f(x) = x. Graph both functions on the same coordinate plane. 1) g(x)=f(x)+4 3) g(x)= -f(x) 30 2) g(x)=√(x) -10 -8. Praes +8 10 -30 4) g(x)=3√(x) 10 5 Paus 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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**Title: Exploring Transformations in Linear Functions** **Instructions: Determine the graph for each \( g(x) \) function if the parent function is \( f(x) = x \). Graph both functions on the same coordinate plane.** 1) **\( g(x) = f(x) + 4 \)** - **Explanation**: This is a vertical translation of the parent function \( f(x) = x \) upwards by 4 units. 2) **\( g(x) = \frac{1}{3} f(x) \)** - **Explanation**: This transformation compresses the graph of \( f(x) = x \) vertically by a factor of \(\frac{1}{3}\). 3) **\( g(x) = -f(x) \)** - **Explanation**: This reflection occurs over the x-axis, transforming \( f(x) = x \) to \( -f(x) \). 4) **\( g(x) = 3f(x) \)** - **Explanation**: This transformation stretches the graph of \( f(x) = x \) vertically by a factor of 3. **Graph Descriptions**: - All graphs display a set of axes with a grid showing increments from -10 to 10 on both axes. - Each graph illustrates the parent function \( f(x) = x \) as a diagonal line through the origin, \( (0,0) \). 1. **Graph 1**: Shows two lines. The line representing \( g(x) = f(x) + 4 \) is parallel to and above \( f(x) = x \). 2. **Graph 2**: Displays a shallower line below \( f(x) = x \) for \( g(x) = \frac{1}{3} f(x) \). 3. **Graph 3**: Illustrates a line going downward, the reflection \( g(x) = -f(x) \), mirroring \( f(x) = x \). 4. **Graph 4**: Depicts a steeper line for \( g(x) = 3f(x) \), vertically stretching the parent. These transformations highlight how altering the equation of a function can affect its graph’s appearance.
Transcribed Image Text:**Title: Exploring Transformations in Linear Functions** **Instructions: Determine the graph for each \( g(x) \) function if the parent function is \( f(x) = x \). Graph both functions on the same coordinate plane.** 1) **\( g(x) = f(x) + 4 \)** - **Explanation**: This is a vertical translation of the parent function \( f(x) = x \) upwards by 4 units. 2) **\( g(x) = \frac{1}{3} f(x) \)** - **Explanation**: This transformation compresses the graph of \( f(x) = x \) vertically by a factor of \(\frac{1}{3}\). 3) **\( g(x) = -f(x) \)** - **Explanation**: This reflection occurs over the x-axis, transforming \( f(x) = x \) to \( -f(x) \). 4) **\( g(x) = 3f(x) \)** - **Explanation**: This transformation stretches the graph of \( f(x) = x \) vertically by a factor of 3. **Graph Descriptions**: - All graphs display a set of axes with a grid showing increments from -10 to 10 on both axes. - Each graph illustrates the parent function \( f(x) = x \) as a diagonal line through the origin, \( (0,0) \). 1. **Graph 1**: Shows two lines. The line representing \( g(x) = f(x) + 4 \) is parallel to and above \( f(x) = x \). 2. **Graph 2**: Displays a shallower line below \( f(x) = x \) for \( g(x) = \frac{1}{3} f(x) \). 3. **Graph 3**: Illustrates a line going downward, the reflection \( g(x) = -f(x) \), mirroring \( f(x) = x \). 4. **Graph 4**: Depicts a steeper line for \( g(x) = 3f(x) \), vertically stretching the parent. These transformations highlight how altering the equation of a function can affect its graph’s appearance.
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