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warpedkitten

  • one year ago

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?

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  1. Vocaloid
    • one year ago
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    hint: f(x) is odd, so #of points in Q1 = #of points in Q3

  2. Vocaloid
    • one year ago
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    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?

  3. warpedkitten
    • one year ago
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    6?

  4. misty1212
    • one year ago
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    HI!

  5. misty1212
    • one year ago
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    if six are in quadrant 1, and it is odd, then 6 are in quadrant 3 right?

  6. misty1212
    • one year ago
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    that leaves \(14-6=8\) to split between quadrant 2 and 4

  7. misty1212
    • one year ago
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    if it is odd, however many you see in quadrant 2, you see in quadrant 4 so halve of the remaining 8

  8. misty1212
    • one year ago
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    *half

  9. warpedkitten
    • one year ago
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    So 4?

  10. misty1212
    • one year ago
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    that is what i get, yes

  11. misty1212
    • one year ago
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    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

  12. warpedkitten
    • one year ago
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    Thank you. :)

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