determine wheather the graph of each function is symmetric with respect to the origin... 1.f(x)=-2x
A function which is symmetric with respect to the origin is an odd function. That is to say that f(-x) = -f(x). In other words, the function for values less than zero is upside down compared to values greater than zero. This is a classic example of an odd function: http://en.wikipedia.org/wiki/File:Function_x%5E3.svg. So let's try and see if f(-x) = -f(x) What does f(-x) equal? -2(-x) = 2x What does -f(x) equal? -(-2x)=2x They are the same. So based on our definition of odd functions - those which are symmetric about the origin - f(-x) =-f(x), this function is in fact odd. Does this help?
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