Properties of Odd and Even Functions

0313phd

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Joined
Apr 21, 2011
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I just wanted to make sure I solved this one with the correct reasoning.
PROBLEM: First, I was shown some values of the function h, which is defined for all real numbers x. If h is an
odd function, what is the value of c? I can't seem to duplicate the table that I was shown, here in html, but the values are as follows:
first point: x= 3, h(x)=-5; second point: x=-2, h(x)=-4; third point: x=2, c=?

First, I graphed the points to get some notion of what kind of odd function it was. Since, even functions have symmetry across the y axis, and odd functions have symmetry across the x axis, I based my choice on what would give greater symmetry across the x axis. c was 4, and that was the right answer, but did I think about it in the most efficient way? I could also do this algrebraically with f(-x)= -f(x) or -f(-2) or 2 and f(-x)=-f(x)= -f(-4)= or 4. I appreciate knowing my mistakes. 0313
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0313phd said:
I just wanted to make sure I solved this one with the correct reasoning.
PROBLEM: First, I was shown some values of the function h, which is defined for all real numbers x. If h is an
odd function, what is the value of c? I can't seem to duplicate the table that I was shown, here in html, but the values are as follows:
first point: x= 3, h(x)=-5; second point: x=-2, h(x)=-4; third point: x=2, c=? I am very confused by the question. You have said that h(x) is an odd function, but you have not said what c is. If c = h(x), then graphing is not necessary: by the definition of an odd function, h(x) = - h(- x) so h(2) = - h( - 2) = - (- 4) = 4. I apologize if c has some conventional definition that I am supposed to know.
 
I think they want me to assume that c =h(x) because it is in the h(x) column on the graph I duplicated. Thank you
 
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