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Hello I always have issues with these graphs for some reason! The question is "give the graphs of f(x) and g(x) below, find the composition of functions f(g(-1)). I think the thing that is confusing me is what we are looking for.

Hello I always have issues with these graphs for some reason! The question is "give the graphs of f(x) and g(x) below, find the composition of functions f(g(-1)). I think the thing that is confusing me is what we are looking for.

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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Hello I always have issues with these graphs for some reason! The question is "give the graphs of f(x) and g(x) below, find the composition of functions f(g(-1)). I think the thing that is confusing me is what we are looking for.
The image depicts two graphs plotted on a coordinate plane, representing functions labeled \( f(x) \) and \( g(x) \). Here’s a detailed breakdown: ### Graph Descriptions 1. **Graph of \( f(x) \)**: - **Color**: Red - **Shape**: Parabolic curve opening upwards. - **Axes**: - **X-axis intersection**: The curve intersects the x-axis around \( x = -3 \) and again near \( x = 1 \). - **Y-axis behavior**: The parabola passes slightly below the y-axis. 2. **Graph of \( g(x) \)**: - **Color**: Blue - **Shape**: Parabolic curve opening downwards. - **Axes**: - **Vertex**: The highest point of the curve appears to be around \( x = 3 \), \( y = 13 \). - **X-axis intersection**: It intersects the x-axis between \( x = 0 \) and \( x = 6 \). ### Coordinate System - **X-Axis**: Labeled with increments from \( -9 \) to \( 9 \). - **Y-Axis**: Labeled with increments from \( 0 \) to \( 13 \). ### General Observations - The graph of \( f(x) \) features a minimum point, indicating it’s a quadratic function with a positive leading coefficient. - The graph of \( g(x) \) features a maximum point, indicating it’s a quadratic function with a negative leading coefficient. - The two parabolas intersect near the point where \( x = 1 \). This illustration helps in understanding the behavior of quadratic functions and their graphical characteristics, such as intercepts and vertex positions.
Transcribed Image Text:The image depicts two graphs plotted on a coordinate plane, representing functions labeled \( f(x) \) and \( g(x) \). Here’s a detailed breakdown: ### Graph Descriptions 1. **Graph of \( f(x) \)**: - **Color**: Red - **Shape**: Parabolic curve opening upwards. - **Axes**: - **X-axis intersection**: The curve intersects the x-axis around \( x = -3 \) and again near \( x = 1 \). - **Y-axis behavior**: The parabola passes slightly below the y-axis. 2. **Graph of \( g(x) \)**: - **Color**: Blue - **Shape**: Parabolic curve opening downwards. - **Axes**: - **Vertex**: The highest point of the curve appears to be around \( x = 3 \), \( y = 13 \). - **X-axis intersection**: It intersects the x-axis between \( x = 0 \) and \( x = 6 \). ### Coordinate System - **X-Axis**: Labeled with increments from \( -9 \) to \( 9 \). - **Y-Axis**: Labeled with increments from \( 0 \) to \( 13 \). ### General Observations - The graph of \( f(x) \) features a minimum point, indicating it’s a quadratic function with a positive leading coefficient. - The graph of \( g(x) \) features a maximum point, indicating it’s a quadratic function with a negative leading coefficient. - The two parabolas intersect near the point where \( x = 1 \). This illustration helps in understanding the behavior of quadratic functions and their graphical characteristics, such as intercepts and vertex positions.
The image presents a multiple-choice question related to functions. The question is asking the user to select the correct value of \( f(g(-1)) \) from the options below: - \( f(g(-1)) = 1 \) - \( f(g(-1)) = 7 \) - \( f(g(-1)) = -1 \) - \( f(g(-1)) = 11 \) - \( f(g(-1)) = -4 \) There are no graphs or diagrams in the image. The context suggests a nested function evaluation where \( g(x) \) is input into function \( f(x) \) to determine the final result. The correct answer needs to be selected.
Transcribed Image Text:The image presents a multiple-choice question related to functions. The question is asking the user to select the correct value of \( f(g(-1)) \) from the options below: - \( f(g(-1)) = 1 \) - \( f(g(-1)) = 7 \) - \( f(g(-1)) = -1 \) - \( f(g(-1)) = 11 \) - \( f(g(-1)) = -4 \) There are no graphs or diagrams in the image. The context suggests a nested function evaluation where \( g(x) \) is input into function \( f(x) \) to determine the final result. The correct answer needs to be selected.
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