锟斤拷锟斤拷锟斤拷锟絈锟斤拷锟絵锟角革拷锟叫旓拷(sh锟斤拷)锟絎(xu锟斤拷)锟斤拷锟斤拷要锟斤拷(n锟斤拷i)锟斤拷之一锟斤拷锟节高匡拷锟斤拷(sh锟斤拷)锟絎(xu锟斤拷)試锟絵锟叫筹拷锟斤拷锟紽(xi锟斤拷n)一些锟斤拷(g锟斤拷u)思锟铰穎锟解法锟絗锟斤拷膶锟斤拷Q锟斤拷锟絵锟斤拷锟斤拷使锟斤拷锟絈锟斤拷锟絵锟斤拷知锟絉(sh锟斤拷)系锟統(t锟斤拷ng)锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟铰歸锟絳锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷一锟斤拷锟絚(di锟斤拷n)锟絇(gu锟斤拷n)锟斤拷锟斤拷知锟絚(di锟斤拷n)锟斤拷锟斤拷知直锟斤拷锟斤拷锟絈锟絚(di锟斤拷n)锟斤拷锟絵
锟斤拷锟斤拷
锟斤拷锟斤拷1锟斤拷锟絆(sh锟斤拷)锟絚(di锟斤拷n)P(x锟斤拷y)锟絇(gu锟斤拷n)锟斤拷锟絚(di锟斤拷n)(a,b)锟斤拷锟絈锟絚(di锟斤拷n)锟斤拷P′(x′锟斤拷y′)锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷x′=2a-x
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷锟斤拷锟絚(di锟斤拷n)锟斤拷锟斤拷(bi锟斤拷o)锟斤拷式锟缴得ｏ拷y′=2b-y
锟斤拷锟斤拷
锟斤拷锟斤拷2锟斤拷锟絚(di锟斤拷n)P(x锟斤拷y)锟絇(gu锟斤拷n)锟斤拷直锟斤拷L锟斤拷Ax+By+C=O锟侥岋拷锟絈锟絚(di锟斤拷n)锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷x′=x-(Ax+By+C)
锟斤拷锟斤拷
锟斤拷锟斤拷P′(x′锟斤拷y′)锟絫
锟斤拷锟斤拷
锟斤拷锟斤拷y′=y-(AX+BY+C)
锟斤拷锟斤拷
锟斤拷锟斤拷锟铰岋拷(sh锟斤拷)锟较ｏ拷锟斤拷PP′⊥L锟斤拷PP′锟斤拷锟斤拷锟絚(di锟斤拷n)锟斤拷直锟斤拷L锟较ｏ拷锟缴得ｏ拷Ax′+By′=-Ax-By-2C
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷朔锟斤拷探M锟缴得結(ji锟斤拷)論锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷(- )=-1(B≠0)
锟斤拷锟斤拷
锟斤拷锟斤拷锟截別锟截ｏ拷锟絚(di锟斤拷n)P(x锟斤拷y)锟絇(gu锟斤拷n)锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷1锟斤拷x锟絊锟斤拷y锟絊锟侥岋拷锟絈锟絚(di锟斤拷n)锟街別锟斤拷(x锟斤拷-y)锟斤拷(-x锟斤拷y)
锟斤拷锟斤拷
锟斤拷锟斤拷2锟斤拷直锟斤拷x=a锟斤拷y=a锟侥岋拷锟斤拷(bi锟斤拷o)锟絚(di锟斤拷n)锟街別锟斤拷(2a-x锟斤拷y)锟斤拷(x锟斤拷2a-y)
锟斤拷锟斤拷
锟斤拷锟斤拷3锟斤拷直锟斤拷y=x锟斤拷y=-x锟侥岋拷锟絈锟絚(di锟斤拷n)锟街別锟斤拷(y锟斤拷x)锟斤拷(-y锟斤拷-x)
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷1 锟解線锟斤拷A(3,4)锟絣(f锟斤拷)锟斤拷锟斤拷(j锟斤拷ng)锟絕直锟斤拷x-2y=0锟斤拷锟斤拷锟斤拷锟劫斤拷(j锟斤拷ng)锟絕y锟絊锟斤拷锟戒，锟斤拷锟斤拷饩�锟斤拷(j锟斤拷ng)锟絕锟絚(di锟斤拷n)B(1,5)锟斤拷锟斤拷锟斤拷锟斤拷y锟絊锟斤拷姆锟斤拷渚�锟斤拷锟节碉拷直锟斤拷锟斤拷锟斤拷锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷锟解：锟斤拷D锟斤拷锟缴癸拷式锟斤拷锟斤拷锟紸锟絇(gu锟斤拷n)锟斤拷直锟斤拷x-2y=0锟侥岋拷锟絈锟絚(di锟斤拷n)
锟斤拷锟斤拷
锟斤拷锟斤拷A′(5,0)锟斤拷B锟絇(gu锟斤拷n)锟斤拷y锟絊锟斤拷锟絈锟絚(di锟斤拷n)B′锟斤拷(-1,5)锟斤拷直锟斤拷A′B′锟侥凤拷锟教烇拷5x+6y-25=0
锟斤拷锟斤拷
锟斤拷锟�锟斤拷锟紺(0, )
锟斤拷锟斤拷
锟斤拷锟�锟斤拷锟街憋拷锟紹C锟侥凤拷锟教為：5x-6y+25=0
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟絇(gu锟斤拷n)锟斤拷锟斤拷知锟絚(di锟斤拷n)锟斤拷锟斤拷知直锟斤拷锟侥岋拷锟絈锟斤拷锟斤拷锟斤拷锟絵
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷锟斤拷知锟斤拷锟斤拷F(x锟斤拷y)=0锟絇(gu锟斤拷n)锟斤拷锟斤拷知锟絚(di锟斤拷n)锟斤拷锟斤拷知直锟斤拷锟侥岋拷锟絈锟斤拷锟斤拷锟斤拷锟教時(sh锟斤拷)锟斤拷只須岋拷锟斤拷锟斤拷F(x锟斤拷y)=O锟斤拷锟斤拷锟斤拷一锟絚(di锟斤拷n)(x锟斤拷y)锟絇(gu锟斤拷n)锟斤拷锟斤拷知锟絚(di锟斤拷n)锟斤拷锟斤拷知直锟斤拷锟侥岋拷锟絈锟絚(di锟斤拷n)锟斤拷锟斤拷锟斤拷(bi锟斤拷o)锟斤拷Q锟斤拷锟斤拷F(x锟斤拷y)=0锟斤拷锟斤拷锟斤拷(y锟斤拷ng)锟斤拷锟斤拷锟絈锟斤拷锟斤拷锟斤拷锟缴达拷锟揭傦拷锟矫筹拷锟斤拷锟铰結(ji锟斤拷)論锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷1锟斤拷锟斤拷锟斤拷F(x锟斤拷y)=0锟絇(gu锟斤拷n)锟斤拷锟絚(di锟斤拷n)(a,b)锟侥岋拷锟絈锟斤拷锟斤拷锟侥凤拷锟斤拷锟斤拷F(2a-x锟斤拷2b-y)=0
锟斤拷锟斤拷
锟斤拷锟斤拷2锟斤拷锟斤拷锟斤拷F(x锟斤拷y)=0锟絇(gu锟斤拷n)锟斤拷直锟斤拷Ax+By+C=0锟斤拷锟絈锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷F(x-(Ax+By+C)锟斤拷y-(Ax+By+C))=0
锟斤拷锟斤拷
锟斤拷锟斤拷锟截別锟斤拷锟斤拷锟斤拷锟斤拷F(x锟斤拷y)=0锟絇(gu锟斤拷n)锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷(1)x锟絊锟斤拷y锟絊锟斤拷锟絈锟斤拷锟斤拷锟斤拷锟斤拷锟教分別锟斤拷F(x锟斤拷-y)锟斤拷F(-x锟斤拷y)=0
锟斤拷锟斤拷
锟斤拷锟斤拷(2)锟絇(gu锟斤拷n)锟斤拷直锟斤拷x=a锟斤拷y=a锟斤拷锟絈锟斤拷锟斤拷锟斤拷锟斤拷锟教分別锟斤拷F(2a-x锟斤拷y)=0锟斤拷F(x锟斤拷2a-y)=0
锟斤拷锟斤拷
锟斤拷锟斤拷(3)锟絇(gu锟斤拷n)锟斤拷直锟斤拷y=x锟斤拷y=-x锟斤拷锟絈锟斤拷锟斤拷锟斤拷锟斤拷锟教分別锟斤拷F(y锟斤拷x)=0锟斤拷F(-y锟斤拷-x)=0
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷還锟斤拷锟斤拷锟铰兩傦拷(g锟斤拷)锟結(ji锟斤拷)論锟斤拷锟斤拷锟斤拷锟斤拷(sh锟斤拷)y=f(x)锟侥圖锟斤拷锟斤拷锟�锟斤拷去锟斤拷y锟絊锟斤拷邊锟紻锟斤拷锟斤拷锟斤拷锟斤拷y锟絊锟斤拷邊锟侥圖锟斤拷锟斤拷锟斤拷锟斤拷锟絇(gu锟斤拷n)锟斤拷y锟絊锟侥岋拷锟絈锟紻锟斤拷玫锟統(t锟斤拷ng)=f(|x|)锟侥圖锟斤拷锟斤拷锟斤拷锟斤拷x锟絊锟较凤拷锟紻锟襟，岋拷x锟絊锟铰凤拷锟紻锟斤拷锟斤拷锟斤拷去锟矫碉拷y(t锟斤拷ng)=|f(x)|锟侥圖锟斤拷锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷2(全锟斤拷锟竭匡拷試锟絵)锟絆(sh锟斤拷)锟斤拷锟斤拷C锟侥凤拷锟斤拷锟斤拷y=x3-x锟斤拷锟斤拷C锟斤拷x锟絊y锟絊锟斤拷锟斤拷謩e平锟斤拷锟狡勶拷(d锟斤拷ng)t锟斤拷s锟斤拷位锟絃锟饺猴拷锟斤拷锟斤拷锟紺1锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷1)锟斤拷锟斤拷锟斤拷锟斤拷C1锟侥凤拷锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷2)锟紺锟斤拷锟斤拷锟斤拷C锟絚C1锟絇(gu锟斤拷n)锟斤拷锟絚(di锟斤拷n)A( , )锟斤拷锟絈锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷(1)锟斤拷 知C1锟侥凤拷锟教烇拷y=(x-t)3-(x-t)+s
锟斤拷锟斤拷
锟斤拷锟斤拷(2)锟紺锟斤拷 锟斤拷锟斤拷锟斤拷C锟斤拷锟斤拷取一锟絚(di锟斤拷n)B(a,b)锟斤拷锟絆(sh锟斤拷)B1(a1,b1)锟斤拷B锟絇(gu锟斤拷n)锟斤拷A锟侥岋拷锟絈锟絚(di锟斤拷n)锟斤拷锟斤拷a=t-a1锟斤拷b=s-b1锟斤拷锟斤拷锟斤拷C锟侥凤拷锟教得ｏ拷
锟斤拷锟斤拷
锟斤拷锟斤拷s-b1=(t-a1)3-(t-a1)
锟斤拷锟斤拷
锟斤拷锟�锟斤拷锟絙1=(a1-t)3-(a1-t)+s
锟斤拷锟斤拷
锟斤拷锟�锟斤拷锟紹1(a1,b1)锟組锟斤拷C1锟侥凤拷锟斤拷
锟斤拷锟斤拷
锟斤拷锟�锟斤拷锟紹1锟斤拷锟斤拷锟斤拷C1锟斤拷锟斤拷锟斤拷之锟斤拷锟紺锟斤拷锟斤拷锟斤拷C1锟较碉拷锟絚(di锟斤拷n)锟絇(gu锟斤拷n)锟斤拷锟絚(di锟斤拷n)A锟侥岋拷锟絈锟絚(di锟斤拷n)锟斤拷锟斤拷锟斤拷C锟斤拷
锟斤拷锟斤拷
锟斤拷锟�锟斤拷锟斤拷锟斤拷锟紺锟斤拷C1锟絇(gu锟斤拷n)锟斤拷a锟斤拷锟絈
锟斤拷锟斤拷
锟斤拷锟斤拷锟揭傦拷锟斤拷前锟斤拷慕Y(ji锟斤拷)論锟斤拷锟紺锟斤拷锟絚(di锟斤拷n)P(x,y)锟絇(gu锟斤拷n)锟斤拷A锟侥岋拷锟絈锟絚(di锟斤拷n)锟斤拷P1(t-x,s-y)锟斤拷锟斤拷锟斤拷锟斤拷锟紺锟絇(gu锟斤拷n)锟斤拷A锟侥岋拷锟絈锟斤拷锟斤拷锟揭傦拷锟斤拷锟斤拷锟斤拷锟斤拷(bi锟斤拷o)锟斤拷锟斤拷C锟侥凤拷锟斤拷锟斤拷锟矫ｏ拷s-y=(t-x)3-(t-x)
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷y=(x-t)3-(x-t)+s
锟斤拷锟斤拷
锟斤拷锟斤拷锟剿硷拷锟斤拷C1锟侥凤拷锟斤拷锟斤拷锟斤拷C锟絇(gu锟斤拷n)锟斤拷A锟侥岋拷锟絈锟斤拷锟斤拷锟斤拷锟斤拷C1锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟侥岋拷锟絈锟斤拷锟絵
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷锟斤拷F(x,y)=0锟斤拷(锟斤拷锟侥伙拷锟絊)锟斤拷锟絈锟斤拷锟斤拷锟侥筹拷要锟絣锟斤拷锟斤拷锟斤拷锟斤拷F(x,y)=0锟斤拷锟斤拷锟斤拷一锟絚(di锟斤拷n)P(x,y)(锟絇(gu锟斤拷n)锟节岋拷锟絈锟斤拷锟侥伙拷?q锟斤拷)锟斤拷Q锟絊)锟侥岋拷锟絈锟絚(di锟斤拷n)锟斤拷锟斤拷锟斤拷(bi锟斤拷o)锟斤拷Q锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷(y锟斤拷ng)锟斤拷锟斤拷锟斤拷(bi锟斤拷o)锟襟方程诧拷變锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷锟界拋锟斤線y2=-8x锟斤拷锟斤拷一锟絚(di锟斤拷n)p(x,y)锟絚x锟絊锟斤拷y=0锟侥岋拷锟絈锟絚(di锟斤拷n)p′(x,-y)锟斤拷锟斤拷锟斤拷锟斤拷(bi锟斤拷o)也锟組锟姐方锟斤拷y2=-8x锟斤拷锟斤拷y2=-8x锟絇(gu锟斤拷n)锟斤拷x锟絊锟斤拷锟絈锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷3 锟斤拷锟斤拷xy2-x2y=2x锟斤拷锟斤拷示锟斤拷锟斤拷锟斤拷锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷A锟斤拷锟絇(gu锟斤拷n)锟斤拷y锟絊锟斤拷锟絈 B锟斤拷锟絇(gu锟斤拷n)锟斤拷直锟斤拷x+y=0锟斤拷锟絈
锟斤拷锟斤拷
锟斤拷锟斤拷C锟斤拷锟絇(gu锟斤拷n)锟斤拷原锟絚(di锟斤拷n)锟斤拷锟絈 D锟斤拷锟絇(gu锟斤拷n)锟斤拷直锟斤拷x-y=0锟斤拷锟絈
锟斤拷锟斤拷
锟斤拷锟斤拷锟解：锟节凤拷锟斤拷锟斤拷锟斤拷-x锟絈x锟斤拷同锟絩(sh锟斤拷)锟斤拷-y锟絈y锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷(-x)(-y)2-(-x)2(-y)=-2x锟斤拷锟斤拷xy2-x2y=2x锟斤拷锟教诧拷變
锟斤拷锟斤拷
锟斤拷锟�锟斤拷锟斤拷锟斤拷锟斤拷P(gu锟斤拷n)锟斤拷原锟絚(di锟斤拷n)锟斤拷锟絈锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷锟斤拷锟斤拷(sh锟斤拷)锟紻锟斤拷锟斤拷锟絇(gu锟斤拷n)锟斤拷直锟斤拷锟斤拷锟絚(di锟斤拷n)锟侥岋拷锟絈锟斤拷锟絵锟揭傦拷锟斤拷锟斤拷锟铰幾傦拷(g锟斤拷)锟斤拷要锟結(ji锟斤拷)論锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷1锟斤拷锟斤拷锟斤拷(sh锟斤拷)f(x)锟斤拷锟絰锟斤拷锟斤拷R锟斤拷a锟介常锟斤拷(sh锟斤拷)锟斤拷锟斤拷锟斤拷锟斤拷x∈R锟斤拷锟斤拷锟斤拷f(a+x)=f(a-x)锟斤拷锟絫y=f(x)锟侥圖锟斤拷锟絇(gu锟斤拷n)锟斤拷x=a锟斤拷锟絈锟斤拷
锟斤拷锟斤拷
锟斤拷锟斤拷锟紷锟斤拷锟斤拷?y锟斤拷n)锟絘+x锟斤拷a-x锟紷锟斤拷锟絚(di锟斤拷n)锟街別锟斤拷锟斤拷a锟斤拷锟斤拷锟揭冿拷邊锟斤拷锟絇(gu锟斤拷n)锟斤拷a锟斤拷锟絈锟斤拷锟斤拷锟戒函锟斤拷(sh锟斤拷)值锟斤拷锟�锟斤拷锟絝锟斤拷锟紷锟斤拷锟絚(di锟斤拷n)锟絇(gu锟斤拷n)锟斤拷直锟斤拷x=a锟斤拷锟絈锟斤拷锟斤拷x锟斤拷锟斤拷锟斤拷锟皆可得結(ji锟斤拷)論锟斤拷
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锟斤拷锟斤拷锟斤拷锟界對锟斤拷f(x)锟斤拷t∈R锟斤拷锟斤拷f(2+t)=f(2-t)锟絫f(x)锟紻锟斤拷锟絇(gu锟斤拷n)锟斤拷x=2锟斤拷锟絈锟斤拷锟紧將條锟斤拷锟侥烇拷f(1+t)=f(3-t)锟斤拷 f(t)=f(4-t)锟結(ji锟斤拷)論锟斤拷锟斤拷锟斤拷兀锟斤拷锟揭皇斤拷锟斤拷锟絫=1+m锟絫锟斤拷f(2+m)=f(2-m)锟斤拷锟节讹拷式锟斤拷锟斤拷t=2+m锟斤拷也锟斤拷f(2+m)=f(2-m)锟斤拷锟斤拷锟斤拷锟斤拷锟斤拷同锟接結(ji锟斤拷)論锟斤拷锟絇(gu锟斤拷n)锟斤拷x=2锟斤拷锟絈锟斤拷锟缴达拷锟揭傦拷锟矫筹拷锟斤拷锟铰的革拷一锟斤拷慕Y(ji锟斤拷)論锟斤拷
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锟斤拷锟斤拷2锟斤拷锟斤拷锟斤拷(sh锟斤拷)f(x)锟斤拷锟絰锟斤拷?y锟斤拷n)锟絉锟斤拷a锟斤拷b锟介常锟斤拷(sh锟斤拷)锟斤拷锟斤拷锟斤拷锟斤拷x∈R锟斤拷锟斤拷f(a+x)=f(b-x)锟斤拷锟絫锟斤拷D锟斤拷锟絇(gu锟斤拷n)锟斤拷直锟斤拷x= 锟斤拷锟絈锟斤拷
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锟斤拷锟斤拷锟揭傦拷锟劫侊拷探討锟斤拷锟铰嗭拷锟絵锟斤拷锟紧將條锟斤拷锟侥烇拷f(2+t)=-f(2-t)锟結(ji锟斤拷)論锟斤拷锟斤拷锟斤拷兀锟皆囷拷锟斤拷锟斤拷2锟侥筹拷0锟斤拷話锟斤拷f(t)=-f(t)锟紷锟斤拷锟芥函锟斤拷(sh锟斤拷)锟斤拷锟紻锟斤拷锟絇(gu锟斤拷n)锟斤拷(0,0)锟斤拷锟斤拷锟侥岋拷锟絈锟斤拷锟紽(xi锟斤拷n)锟斤拷锟斤拷f(2+t)=-f(2-t)锟斤拷锟斤拷锟狡斤拷锟�锟斤拷锟缴达拷锟揭傦拷锟斤拷锟斤拷锟斤拷锟紻锟斤拷锟絇(gu锟斤拷n)锟斤拷M(2锟斤拷0)锟斤拷锟斤拷锟侥岋拷锟絈锟斤拷锟斤拷D锟斤拷取锟絚(di锟斤拷n) A(2+t锟斤拷f(2+t))锟斤拷锟絇(gu锟斤拷n)锟斤拷M(2锟斤拷0)锟侥岋拷锟絈锟絚(di锟斤拷n)锟斤拷A′(2-x锟斤拷-f(2+x))
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锟斤拷锟斤拷锟斤拷-f(2+X)=f(2-x)锟斤拷A′锟斤拷锟斤拷锟斤拷(bi锟斤拷o)锟斤拷(2-x锟斤拷f(2-x))锟紷然锟节圖锟斤拷锟斤拷
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锟斤拷锟斤拷锟紧將條锟斤拷锟侥烇拷f(x)=-f(4-x)锟結(ji锟斤拷)論一锟斤拷锟斤拷锟狡廣锟斤拷一锟斤拷傻锟斤拷锟斤拷锟斤拷锟揭�锟結(ji锟斤拷)論锟斤拷
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