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?

Question

vocaloid · Answer

hint:

f(x) is odd, so #of points in Q1 = #of points in Q3

vocaloid · Answer

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 · Answer

6?

misty1212 · Answer

HI!

misty1212 · Answer

if six are in quadrant 1, and it is odd, then 6 are in quadrant 3 right?

misty1212 · Answer

that leaves $14-6=8$ to split between quadrant 2 and 4

misty1212 · Answer

if it is odd, however many you see in quadrant 2, you see in quadrant 4 so halve of the remaining 8

misty1212 · Answer

*half

warpedkitten · Answer

So 4?

misty1212 · Answer

that is what i get, yes

misty1212 · Answer

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 · Answer

Thank you. :)