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Determine the symmetry of each function. < < Neither Odd Even 1. 2. y = = 3. -8 16 3x x²-5 0

Determine the symmetry of each function. < < Neither Odd Even 1. 2. y = = 3. -8 16 3x x²-5 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 35E
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## Determine the Symmetry of Each Function Instructions: For each function provided, determine whether it is neither symmetric, odd-symmetric, or even-symmetric. Use the dropdown options to make your selection. ### Function 1 - **Graph Description:** The graph of function 1 is a vertical hyperbola symmetric with respect to the y-axis. The curve approaches the y-axis asymptotically from both the left and right sides and moves downwards. - **Select Symmetry:** - Neither - Odd - Even ### Function 2 \[ y = \frac{3x}{x^2 - 5} \] - **Graph Description:** This function's symmetry needs to be determined algebraically and by its graphical representation. The function has both horizontal and vertical asymptotes and exhibits behavior indicative of either odd or neither type of symmetry. - **Select Symmetry:** - Neither - Odd - Even ### Function 3 - **Graph Description:** The graph of function 3 is a rational function with horizontal and vertical asymptotes. It appears to have rotational symmetry about the origin, indicating either odd symmetry or neither symmetry. - **Select Symmetry:** - Neither - Odd - Even ### Dropdown Selection Each function's symmetry can be selected from the dropdown options provided to the left of each function description. After careful analysis of the graph and the equation, make your selections accordingly. ### Tips for Determining Symmetry: - **Odd Function:** A function \( f(x) \) is odd if \( f(-x) = -f(x) \). - **Even Function:** A function \( f(x) \) is even if \( f(-x) = f(x) \).
Transcribed Image Text:## Determine the Symmetry of Each Function Instructions: For each function provided, determine whether it is neither symmetric, odd-symmetric, or even-symmetric. Use the dropdown options to make your selection. ### Function 1 - **Graph Description:** The graph of function 1 is a vertical hyperbola symmetric with respect to the y-axis. The curve approaches the y-axis asymptotically from both the left and right sides and moves downwards. - **Select Symmetry:** - Neither - Odd - Even ### Function 2 \[ y = \frac{3x}{x^2 - 5} \] - **Graph Description:** This function's symmetry needs to be determined algebraically and by its graphical representation. The function has both horizontal and vertical asymptotes and exhibits behavior indicative of either odd or neither type of symmetry. - **Select Symmetry:** - Neither - Odd - Even ### Function 3 - **Graph Description:** The graph of function 3 is a rational function with horizontal and vertical asymptotes. It appears to have rotational symmetry about the origin, indicating either odd symmetry or neither symmetry. - **Select Symmetry:** - Neither - Odd - Even ### Dropdown Selection Each function's symmetry can be selected from the dropdown options provided to the left of each function description. After careful analysis of the graph and the equation, make your selections accordingly. ### Tips for Determining Symmetry: - **Odd Function:** A function \( f(x) \) is odd if \( f(-x) = -f(x) \). - **Even Function:** A function \( f(x) \) is even if \( f(-x) = f(x) \).
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