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Problem 71 Hard Difficulty

(a) If the point $ (5 , 3) $ is on the graph of an even function, what other point must also be on the graph?
(b) If the point $ (5 , 3) $ is on the graph of an odd function, what other point must also be on the graph?

Answer

(a) Because an even function is symmetric with respect to the $y$ -axis, and the point (5,3) is on the graph of this even function, the point (-5,3) must also be on its graph.
(b) Because an odd function is symmetric with respect to the origin, and the point (5,3) is on the graph of this odd function, the point (-5,-3) must also be on its graph.

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Video Transcript

suppose we know that the 0.53 is on an even function is on the graph of uneven function. Well, what other point would be on that function? So here's what we know about even functions. They have y axis symmetry. So an example of that could be something like this. Where if you were to fold it along the y axis, it would line up. And that means if you have the 0.53 you must also have the point across the Y axis from it, which would be negative 53 Now, for the other part of the problem, we have an odd function. An odd functions have origin symmetry. So an example of origin Symmetry could be something like this where you have symmetry about the origin, like a 180 degree turn. So if you have the 0.53 that means you must also have the point. Negative five negative three