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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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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