warpedkitten
  • warpedkitten
The graph of f(x) consists of 14 points. Six of the points lie in Quadrant I of the coordinate plane. If f(x) is an odd function, what is the greatest number of points that can lie in Quadrant II?
Mathematics
katieb
  • katieb
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Vocaloid
  • Vocaloid
hint: f(x) is odd, so #of points in Q1 = #of points in Q3
Vocaloid
  • Vocaloid
6 points in Q1 = 6 points in Q3 this gives us 6+6 = 12 points not in Q2 so if there are 14 points total, how many can be in Q2?
warpedkitten
  • warpedkitten
6?

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misty1212
  • misty1212
HI!
misty1212
  • misty1212
if six are in quadrant 1, and it is odd, then 6 are in quadrant 3 right?
misty1212
  • misty1212
that leaves \(14-6=8\) to split between quadrant 2 and 4
misty1212
  • misty1212
if it is odd, however many you see in quadrant 2, you see in quadrant 4 so halve of the remaining 8
misty1212
  • misty1212
*half
warpedkitten
  • warpedkitten
So 4?
misty1212
  • misty1212
that is what i get, yes
misty1212
  • misty1212
say for example \((-2,3)\) is a point in quadrant 2 on the graph then since \(f\) is odd, that means \((2,-3)\) is also on the graph, and that is in quadrant 4
warpedkitten
  • warpedkitten
Thank you. :)

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