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# A function $f$ has domain $[-5 , 5]$ and a portion of its graph is shown.(a) Complete the graph of $f$ if it is known that $f$ is even.(b) Complete the graph of $f$ if it is known that $f$ is odd.

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

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### Video Transcript

if f isn't even function, that means it has y axis symmetry. So the Y axis is like a fold line. You could match the function up if you folded it along that line. Therefore, the other side of the function must be something like this. Now, if F is odd, that means it has origin symmetry where if you turned it 180 degrees, it would look like it already looks. So in order to do that, we need opposite X values to have opposite Why values and we're going to get something like this.

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##### Kristen K.

University of Michigan - Ann Arbor

##### Samuel H.

University of Nottingham

Lectures

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