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If you were ONLY given the graph of the function, how could you determine if the function was even, odd, or neither? Use at least two sentences to support your answer. Question 4

Ask by Clark Gray. in the United States
Feb 22,2025

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To determine if a function is even, odd, or neither from its graph, check for y-axis symmetry: if reflecting the graph across the y-axis leaves it unchanged, the function is even. If rotating the graph 180 degrees about the origin leaves it unchanged, the function is odd. If neither symmetry is present, the function is neither even nor odd.

Solution

To determine if the function is even, odd, or neither from its graph, first check for y-axis symmetry—if you can reflect the graph across the y-axis and it remains unchanged, then the function is even. Next, check for origin symmetry—if rotating the graph 180 degrees about the origin leaves it unchanged, the function is odd; if neither symmetry condition holds, then the function is neither even nor odd.

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To determine if a function is even, look for symmetry about the y-axis in the graph; if the left side of the graph mirrors the right side, the function is even. Conversely, if the graph has symmetry about the origin (where rotating the graph 180 degrees results in the same graph), then the function is odd; if neither symmetry applies, the function is neither even nor odd.

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