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y = 20x is symmetric about the origin. (If you rotate it around the origin, it will look the same before it is rotated 360 degrees).

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Are all odd functions symmetric about the orizin?

Yes, all odd functions are symmetric about the origin. This means that for any point ((x, f(x))) on the graph of an odd function, the point ((-x, -f(x))) will also be on the graph. This symmetry is defined by the property (f(-x) = -f(x)) for all (x) in the function's domain. Thus, the graph of an odd function exhibits rotational symmetry around the origin.


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An odd function is a type of mathematical function that satisfies the condition ( f(-x) = -f(x) ) for all ( x ) in its domain. This means that the graph of the function is symmetric with respect to the origin; if you rotate the graph 180 degrees around the origin, it remains unchanged. Examples of odd functions include ( f(x) = x^3 ) and ( f(x) = \sin(x) ).


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To determine if a signal is even or odd, you can use the definitions of even and odd functions. A signal ( x(t) ) is considered even if ( x(t) = x(-t) ) for all ( t ), meaning it is symmetric about the y-axis. Conversely, a signal is odd if ( x(t) = -x(-t) ), indicating it is symmetric about the origin. To calculate, you can analyze the signal's mathematical expression or plot it to visually assess its symmetry.