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The graph of a function is given. Decide whether it is even, odd, or neither. 6- 2- -4 -2 4 -2- -4-

The graph of a function is given. Decide whether it is even, odd, or neither. 6- 2- -4 -2 4 -2- -4-

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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### Analyzing Function Symmetry The image displays a graph of a function, which we need to analyze for its symmetry to determine if it is even, odd, or neither. #### Graph Details - **Axes**: The graph is plotted on a Cartesian coordinate system with the x-axis ranging from -4 to 4 and the y-axis from -6 to 6. - **Function Shape**: The function is a smooth curve that oscillates upwards and downwards, akin to a sine or cosine wave. - **Symmetry**: - The graph appears symmetric about the y-axis. This is an indicator of an even function. - Even functions are defined as \( f(x) = f(-x) \) for all values of x in the function’s domain. #### Graph Interpretation - **Intersections**: The graph crosses the y-axis at the value 4. - **Peaks and Valleys**: - Peaks towards positive and negative y-values are symmetric. - The curve achieves similar heights at equivalent distances from the y-axis on either side, further suggesting it is an even function. When analyzing symmetry: - **Even Function**: Symmetric about the y-axis. - **Odd Function**: Symmetric about the origin, meaning \( f(-x) = -f(x) \). - **Neither**: If it doesn’t satisfy conditions for either symmetry. In conclusion, based on the visual symmetry observed in the graph, the function is an even function.
Transcribed Image Text:### Analyzing Function Symmetry The image displays a graph of a function, which we need to analyze for its symmetry to determine if it is even, odd, or neither. #### Graph Details - **Axes**: The graph is plotted on a Cartesian coordinate system with the x-axis ranging from -4 to 4 and the y-axis from -6 to 6. - **Function Shape**: The function is a smooth curve that oscillates upwards and downwards, akin to a sine or cosine wave. - **Symmetry**: - The graph appears symmetric about the y-axis. This is an indicator of an even function. - Even functions are defined as \( f(x) = f(-x) \) for all values of x in the function’s domain. #### Graph Interpretation - **Intersections**: The graph crosses the y-axis at the value 4. - **Peaks and Valleys**: - Peaks towards positive and negative y-values are symmetric. - The curve achieves similar heights at equivalent distances from the y-axis on either side, further suggesting it is an even function. When analyzing symmetry: - **Even Function**: Symmetric about the y-axis. - **Odd Function**: Symmetric about the origin, meaning \( f(-x) = -f(x) \). - **Neither**: If it doesn’t satisfy conditions for either symmetry. In conclusion, based on the visual symmetry observed in the graph, the function is an even function.
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