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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.

see explanation

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Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Boston College

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.