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y=(x-3)cosx
Trazado el gráfico de la función/ y=(x-3)cosx

Gráfico de la función y = y=(x-3)cosx

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = (x - 3)*cos(x)
f(x)=(x−3)cos⁡(x)f{\left(x \right)} = \left(x - 3\right) \cos{\left(x \right)} 
f = (x - 3)*cos(x)
Gráfico de la función
02468-8-6-4-2-1010-2525
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
(x−3)cos⁡(x)=0\left(x - 3\right) \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=3x_{1} = 3
x2=−π2x_{2} = - \frac{\pi}{2}
x3=π2x_{3} = \frac{\pi}{2}
Solución numérica
x1=26.7035375555132x_{1} = 26.7035375555132
x2=64.4026493985908x_{2} = 64.4026493985908
x3=17.2787595947439x_{3} = 17.2787595947439
x4=80.1106126665397x_{4} = 80.1106126665397
x5=−48.6946861306418x_{5} = -48.6946861306418
x6=23.5619449019235x_{6} = 23.5619449019235
x7=−39.2699081698724x_{7} = -39.2699081698724
x8=−86.3937979737193x_{8} = -86.3937979737193
x9=−98.9601685880785x_{9} = -98.9601685880785
x10=36.1283155162826x_{10} = 36.1283155162826
x11=3x_{11} = 3
x12=−51.8362787842316x_{12} = -51.8362787842316
x13=−45.553093477052x_{13} = -45.553093477052
x14=−73.8274273593601x_{14} = -73.8274273593601
x15=−10.9955742875643x_{15} = -10.9955742875643
x16=14.1371669411541x_{16} = 14.1371669411541
x17=−4.71238898038469x_{17} = -4.71238898038469
x18=−14.1371669411541x_{18} = -14.1371669411541
x19=−42.4115008234622x_{19} = -42.4115008234622
x20=−17.2787595947439x_{20} = -17.2787595947439
x21=51.8362787842316x_{21} = 51.8362787842316
x22=−29.845130209103x_{22} = -29.845130209103
x23=70.6858347057703x_{23} = 70.6858347057703
x24=−95.8185759344887x_{24} = -95.8185759344887
x25=92.6769832808989x_{25} = 92.6769832808989
x26=67.5442420521806x_{26} = 67.5442420521806
x27=61.261056745001x_{27} = 61.261056745001
x28=−76.9690200129499x_{28} = -76.9690200129499
x29=10.9955742875643x_{29} = 10.9955742875643
x30=−70.6858347057703x_{30} = -70.6858347057703
x31=58.1194640914112x_{31} = 58.1194640914112
x32=−83.2522053201295x_{32} = -83.2522053201295
x33=−7.85398163397448x_{33} = -7.85398163397448
x34=39.2699081698724x_{34} = 39.2699081698724
x35=54.9778714378214x_{35} = 54.9778714378214
x36=73.8274273593601x_{36} = 73.8274273593601
x37=−80.1106126665397x_{37} = -80.1106126665397
x38=−26.7035375555132x_{38} = -26.7035375555132
x39=7.85398163397448x_{39} = 7.85398163397448
x40=29.845130209103x_{40} = 29.845130209103
x41=−58.1194640914112x_{41} = -58.1194640914112
x42=48.6946861306418x_{42} = 48.6946861306418
x43=76.9690200129499x_{43} = 76.9690200129499
x44=−67.5442420521806x_{44} = -67.5442420521806
x45=83.2522053201295x_{45} = 83.2522053201295
x46=95.8185759344887x_{46} = 95.8185759344887
x47=20.4203522483337x_{47} = 20.4203522483337
x48=32.9867228626928x_{48} = 32.9867228626928
x49=42.4115008234622x_{49} = 42.4115008234622
x50=89.5353906273091x_{50} = 89.5353906273091
x51=86.3937979737193x_{51} = 86.3937979737193
x52=−54.9778714378214x_{52} = -54.9778714378214
x53=−92.6769832808989x_{53} = -92.6769832808989
x54=−36.1283155162826x_{54} = -36.1283155162826
x55=−1.5707963267949x_{55} = -1.5707963267949
x56=−23.5619449019235x_{56} = -23.5619449019235
x57=−64.4026493985908x_{57} = -64.4026493985908
x58=4.71238898038469x_{58} = 4.71238898038469
x59=−20.4203522483337x_{59} = -20.4203522483337
x60=1.5707963267949x_{60} = 1.5707963267949
x61=45.553093477052x_{61} = 45.553093477052
x62=98.9601685880785x_{62} = 98.9601685880785
x63=−32.9867228626928x_{63} = -32.9867228626928
x64=−61.261056745001x_{64} = -61.261056745001
x65=−89.5353906273091x_{65} = -89.5353906273091
Puntos de cruce con el eje de coordenadas Y
El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en (x - 3)*cos(x).
−3cos⁡(0)- 3 \cos{\left(0 \right)}
Resultado:
f(0)=−3f{\left(0 \right)} = -3
Punto:
(0, -3)
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
−(x−3)sin⁡(x)+cos⁡(x)=0- \left(x - 3\right) \sin{\left(x \right)} + \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−78.5520778284944x_{1} = -78.5520778284944
x2=−34.5841198954721x_{2} = -34.5841198954721
x3=−44.0035689215071x_{3} = -44.0035689215071
x4=−25.1682273173293x_{4} = -25.1682273173293
x5=−47.1438297937958x_{5} = -47.1438297937958
x6=−81.6932157658594x_{6} = -81.6932157658594
x7=84.835220716198x_{7} = 84.835220716198
x8=−97.3993321575476x_{8} = -97.3993321575476
x9=12.6694230459213x_{9} = 12.6694230459213
x10=69.130158920116x_{10} = 69.130158920116
x11=31.4510601479335x_{11} = 31.4510601479335
x12=87.9763617358531x_{12} = 87.9763617358531
x13=100.541216632062x_{13} = 100.541216632062
x14=−37.7236626573345x_{14} = -37.7236626573345
x15=25.1778008415242x_{15} = 25.1778008415242
x16=97.3999650893223x_{16} = 97.3999650893223
x17=40.8671065042713x_{17} = 40.8671065042713
x18=−65.9879399974437x_{18} = -65.9879399974437
x19=−28.30626551274x_{19} = -28.30626551274
x20=91.1175349460173x_{20} = 91.1175349460173
x21=−12.6302619891586x_{21} = -12.6302619891586
x22=65.9893200989848x_{22} = 65.9893200989848
x23=−56.5654544420077x_{23} = -56.5654544420077
x24=18.912317780113x_{24} = 18.912317780113
x25=3.95172192033919x_{25} = 3.95172192033919
x26=72.2710660715932x_{26} = 72.2710660715932
x27=−100.540622659664x_{27} = -100.540622659664
x28=94.2587370240534x_{28} = 94.2587370240534
x29=−87.9755858178486x_{29} = -87.9755858178486
x30=44.0066785894522x_{30} = 44.0066785894522
x31=−50.2842475271843x_{31} = -50.2842475271843
x32=−0.294682454486773x_{32} = -0.294682454486773
x33=−94.2580611694573x_{33} = -94.2580611694573
x34=−62.8470386162472x_{34} = -62.8470386162472
x35=−9.50457883886398x_{35} = -9.50457883886398
x36=59.7078928202273x_{36} = 59.7078928202273
x37=56.567333690088x_{37} = 56.567333690088
x38=15.786014834861x_{38} = 15.786014834861
x39=−3.29903328785148x_{39} = -3.29903328785148
x40=62.8485603567807x_{40} = 62.8485603567807
x41=6.55723006500106x_{41} = 6.55723006500106
x42=75.4120326678904x_{42} = 75.4120326678904
x43=−84.8343862178182x_{43} = -84.8343862178182
x44=50.2866269338091x_{44} = 50.2866269338091
x45=81.6941157398245x_{45} = 81.6941157398245
x46=9.57569676385338x_{46} = 9.57569676385338
x47=−18.8951963232073x_{47} = -18.8951963232073
x48=28.3138174685366x_{48} = 28.3138174685366
x49=53.4269031964768x_{49} = 53.4269031964768
x50=47.1465377637573x_{50} = 47.1465377637573
x51=−53.4247959606036x_{51} = -53.4247959606036
x52=−69.1289015588518x_{52} = -69.1289015588518
x53=−40.8634985472455x_{53} = -40.8634985472455
x54=2.22814103089124x_{54} = 2.22814103089124
x55=22.0436114382877x_{55} = 22.0436114382877
x56=78.5530512997373x_{56} = 78.5530512997373
x57=−6.38928965648362x_{57} = -6.38928965648362
x58=−125.671477717255x_{58} = -125.671477717255
x59=−59.7062064512464x_{59} = -59.7062064512464
x60=34.5891650451544x_{60} = 34.5891650451544
x61=−91.1168116486103x_{61} = -91.1168116486103
x62=−72.2699157713744x_{62} = -72.2699157713744
x63=−75.4109763113185x_{63} = -75.4109763113185
x64=37.7278991803885x_{64} = 37.7278991803885
x65=−31.4449502153243x_{65} = -31.4449502153243
x66=−15.7612143304042x_{66} = -15.7612143304042
x67=−22.0310776789363x_{67} = -22.0310776789363
Signos de extremos en los puntos:
(-78.55207782849438, 81.545947468169)

(-34.58411989547207, 37.5708234637983)

(-44.00356892150712, -46.9929350411195)

(-25.168227317329272, -28.1504935824352)

(-47.14382979379579, 50.1338614505173)

(-81.69321576585943, -84.6873127224841)

(84.83522071619804, -81.8291115616385)

(-97.39933215754765, 100.394352415252)

(12.669423045921281, 9.61812478108002)

(69.13015892011602, 66.1225993697551)

(31.45106014793351, 28.4335023766721)

(87.97636173585312, 84.9704783576549)

(100.54121663206242, 97.5360909979324)

(-37.72366265733454, -40.7113903330478)

(25.177800841524213, 22.15529009427)

(97.39996508932231, -94.3946689229274)

(40.867106504271284, -37.8539093345704)

(-65.98793999744368, 68.9806934957898)

(-28.30626551273998, 31.2903064803893)

(91.11753494601734, -88.1118612545098)

(-12.63026198915859, -15.59837063305)

(65.98932009898483, -62.9813837455716)

(-56.56545444200766, -59.5570620887982)

(18.91231778011301, 15.8809883513863)

(3.951721920339186, -0.656121661044172)

(72.2710660715932, -69.2638491787087)

(-100.5406226596642, -103.535793974935)

(94.25873702405337, 91.2532585899567)

(-87.97558581784861, -90.9700903358314)

(44.006678589452186, 40.9944908893309)

(-50.28424752718431, -53.2748663689057)

(-0.2946824544867733, -3.15266324719375)

(-94.25806116945732, -97.2529206150062)

(-62.84703861624724, -65.8394465735594)

(-9.504578838863976, 12.4647842585051)

(59.707892820227336, -56.6990777612809)

(56.56733369008799, 53.558002082243)

(15.786014834860985, -12.7470881005591)

(-3.299033287851476, 6.22112560417095)

(62.84856035678067, 59.840207685858)

(6.557230065001062, 3.42448900708588)

(75.41203266789043, 72.4051287256054)

(-84.83438621781819, 87.828694239774)

(50.28662693380906, 47.2760566650762)

(81.69411573982451, 78.6877627940051)

(9.575696763853385, -6.50095316217611)

(-18.895196323207266, -21.8723959280207)

(28.31381746853661, -25.2940884985806)

(53.42690319647679, -50.4169907777953)

(47.14653776375731, -44.1352162039481)

(-53.424795960603625, 56.4159366951519)

(-69.1289015588518, -72.121970523981)

(-40.863498547245456, 43.8521039892383)

(2.228141030891238, 0.471618974793956)

(22.043611438287677, -19.0174100876084)

(78.55305129973732, -75.5464343027166)

(-6.389289656483623, -9.33648628773909)

(-125.6714777172552, -128.667592028211)

(-59.70620645124642, 62.6982342794497)

(34.589165045154424, -31.5733487197023)

(-91.1168116486103, 94.1114995512231)

(-72.26991577137444, 75.2632738904155)

(-75.41097631131846, -78.4046004308088)

(37.7278991803885, 34.7135104817292)

(-31.444950215324322, -34.4304434690237)

(-15.761214330404183, 18.7346202562976)

(-22.031077678936263, 25.0111263891723)


Intervalos de crecimiento y decrecimiento de la función:
Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
Puntos mínimos de la función:
x1=−44.0035689215071x_{1} = -44.0035689215071
x2=−25.1682273173293x_{2} = -25.1682273173293
x3=−81.6932157658594x_{3} = -81.6932157658594
x4=84.835220716198x_{4} = 84.835220716198
x5=−37.7236626573345x_{5} = -37.7236626573345
x6=97.3999650893223x_{6} = 97.3999650893223
x7=40.8671065042713x_{7} = 40.8671065042713
x8=91.1175349460173x_{8} = 91.1175349460173
x9=−12.6302619891586x_{9} = -12.6302619891586
x10=65.9893200989848x_{10} = 65.9893200989848
x11=−56.5654544420077x_{11} = -56.5654544420077
x12=3.95172192033919x_{12} = 3.95172192033919
x13=72.2710660715932x_{13} = 72.2710660715932
x14=−100.540622659664x_{14} = -100.540622659664
x15=−87.9755858178486x_{15} = -87.9755858178486
x16=−50.2842475271843x_{16} = -50.2842475271843
x17=−0.294682454486773x_{17} = -0.294682454486773
x18=−94.2580611694573x_{18} = -94.2580611694573
x19=−62.8470386162472x_{19} = -62.8470386162472
x20=59.7078928202273x_{20} = 59.7078928202273
x21=15.786014834861x_{21} = 15.786014834861
x22=9.57569676385338x_{22} = 9.57569676385338
x23=−18.8951963232073x_{23} = -18.8951963232073
x24=28.3138174685366x_{24} = 28.3138174685366
x25=53.4269031964768x_{25} = 53.4269031964768
x26=47.1465377637573x_{26} = 47.1465377637573
x27=−69.1289015588518x_{27} = -69.1289015588518
x28=22.0436114382877x_{28} = 22.0436114382877
x29=78.5530512997373x_{29} = 78.5530512997373
x30=−6.38928965648362x_{30} = -6.38928965648362
x31=−125.671477717255x_{31} = -125.671477717255
x32=34.5891650451544x_{32} = 34.5891650451544
x33=−75.4109763113185x_{33} = -75.4109763113185
x34=−31.4449502153243x_{34} = -31.4449502153243
Puntos máximos de la función:
x34=−78.5520778284944x_{34} = -78.5520778284944
x34=−34.5841198954721x_{34} = -34.5841198954721
x34=−47.1438297937958x_{34} = -47.1438297937958
x34=−97.3993321575476x_{34} = -97.3993321575476
x34=12.6694230459213x_{34} = 12.6694230459213
x34=69.130158920116x_{34} = 69.130158920116
x34=31.4510601479335x_{34} = 31.4510601479335
x34=87.9763617358531x_{34} = 87.9763617358531
x34=100.541216632062x_{34} = 100.541216632062
x34=25.1778008415242x_{34} = 25.1778008415242
x34=−65.9879399974437x_{34} = -65.9879399974437
x34=−28.30626551274x_{34} = -28.30626551274
x34=18.912317780113x_{34} = 18.912317780113
x34=94.2587370240534x_{34} = 94.2587370240534
x34=44.0066785894522x_{34} = 44.0066785894522
x34=−9.50457883886398x_{34} = -9.50457883886398
x34=56.567333690088x_{34} = 56.567333690088
x34=−3.29903328785148x_{34} = -3.29903328785148
x34=62.8485603567807x_{34} = 62.8485603567807
x34=6.55723006500106x_{34} = 6.55723006500106
x34=75.4120326678904x_{34} = 75.4120326678904
x34=−84.8343862178182x_{34} = -84.8343862178182
x34=50.2866269338091x_{34} = 50.2866269338091
x34=81.6941157398245x_{34} = 81.6941157398245
x34=−53.4247959606036x_{34} = -53.4247959606036
x34=−40.8634985472455x_{34} = -40.8634985472455
x34=2.22814103089124x_{34} = 2.22814103089124
x34=−59.7062064512464x_{34} = -59.7062064512464
x34=−91.1168116486103x_{34} = -91.1168116486103
x34=−72.2699157713744x_{34} = -72.2699157713744
x34=37.7278991803885x_{34} = 37.7278991803885
x34=−15.7612143304042x_{34} = -15.7612143304042
x34=−22.0310776789363x_{34} = -22.0310776789363
Decrece en los intervalos
[97.3999650893223,∞)\left[97.3999650893223, \infty\right)
Crece en los intervalos
(−∞,−125.671477717255]\left(-\infty, -125.671477717255\right]
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
−((x−3)cos⁡(x)+2sin⁡(x))=0- (\left(x - 3\right) \cos{\left(x \right)} + 2 \sin{\left(x \right)}) = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=−33.0421565872763x_{1} = -33.0421565872763
x2=−17.3765980243604x_{2} = -17.3765980243604
x3=−73.8534450440396x_{3} = -73.8534450440396
x4=20.5339259723255x_{4} = 20.5339259723255
x5=−70.7129603215986x_{5} = -70.7129603215986
x6=−23.6368881258944x_{6} = -23.6368881258944
x7=86.4177690883985x_{7} = 86.4177690883985
x8=51.8771748648305x_{8} = 51.8771748648305
x9=−42.4554715670068x_{9} = -42.4554715670068
x10=0.826862867228188x_{10} = 0.826862867228188
x11=11.2338590161227x_{11} = 11.2338590161227
x12=83.2771138683158x_{12} = 83.2771138683158
x13=−26.770617096282x_{13} = -26.770617096282
x14=70.7153615177027x_{14} = 70.7153615177027
x15=−89.5569955724082x_{15} = -89.5569955724082
x16=55.0163019917346x_{16} = 55.0163019917346
x17=39.3249112691049x_{17} = 39.3249112691049
x18=−58.1521577434381x_{18} = -58.1521577434381
x19=−36.1793185853157x_{19} = -36.1793185853157
x20=5.40591660043711x_{20} = 5.40591660043711
x21=−64.432300083121x_{21} = -64.432300083121
x22=98.9810030297478x_{22} = 98.9810030297478
x23=14.3121594602206x_{23} = 14.3121594602206
x24=−55.0123332166132x_{24} = -55.0123332166132
x25=61.2953513467577x_{25} = 61.2953513467577
x26=73.8556462692966x_{26} = 73.8556462692966
x27=89.5584922796575x_{27} = 89.5584922796575
x28=−92.6978793436777x_{28} = -92.6978793436777
x29=−48.7333266866217x_{29} = -48.7333266866217
x30=48.7383852414105x_{30} = 48.7383852414105
x31=33.053173593001x_{31} = 33.053173593001
x32=45.6000073775805x_{32} = 45.6000073775805
x33=−8.03330382965524x_{33} = -8.03330382965524
x34=−83.2753827526075x_{34} = -83.2753827526075
x35=36.1885045575189x_{35} = 36.1885045575189
x36=−14.2525765162628x_{36} = -14.2525765162628
x37=−61.2921547109207x_{37} = -61.2921547109207
x38=17.4166086363428x_{38} = 17.4166086363428
x39=−1.95446769860329x_{39} = -1.95446769860329
x40=−51.8727106470714x_{40} = -51.8727106470714
x41=−4.9585915020369x_{41} = -4.9585915020369
x42=−76.9940166753296x_{42} = -76.9940166753296
x43=−39.3171352054588x_{43} = -39.3171352054588
x44=80.1365349095748x_{44} = 80.1365349095748
x45=−86.4161615658675x_{45} = -86.4161615658675
x46=95.8401150148972x_{46} = 95.8401150148972
x47=64.4351925360079x_{47} = 64.4351925360079
x48=−11.136122961567x_{48} = -11.136122961567
x49=76.996041906774x_{49} = 76.996041906774
x50=67.5752037953155x_{50} = 67.5752037953155
x51=23.6584567792085x_{51} = 23.6584567792085
x52=29.9192901213547x_{52} = 29.9192901213547
x53=42.462138986437x_{53} = 42.462138986437
x54=−29.9058350256858x_{54} = -29.9058350256858
x55=−67.5725740899573x_{55} = -67.5725740899573
x56=92.6992763110302x_{56} = 92.6992763110302
x57=−98.9797778056003x_{57} = -98.9797778056003
x58=−20.5052352226731x_{58} = -20.5052352226731
x59=26.7874183328987x_{59} = 26.7874183328987
x60=3.09441845244876x_{60} = 3.09441845244876
x61=−95.8388081401923x_{61} = -95.8388081401923
x62=−80.1346653801375x_{62} = -80.1346653801375
x63=−45.5942274137072x_{63} = -45.5942274137072
x64=58.1557091900213x_{64} = 58.1557091900213
x65=8.21987886514604x_{65} = 8.21987886514604

Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
[95.8401150148972,∞)\left[95.8401150148972, \infty\right)
Convexa en los intervalos
(−∞,−95.8388081401923]\left(-\infty, -95.8388081401923\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞((x−3)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to -\infty}\left(\left(x - 3\right) \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
lim⁡x→∞((x−3)cos⁡(x))=⟨−∞,∞⟩\lim_{x \to \infty}\left(\left(x - 3\right) \cos{\left(x \right)}\right) = \left\langle -\infty, \infty\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−∞,∞⟩y = \left\langle -\infty, \infty\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función (x - 3)*cos(x), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞((x−3)cos⁡(x)x)=⟨−1,1⟩\lim_{x \to -\infty}\left(\frac{\left(x - 3\right) \cos{\left(x \right)}}{x}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle x
lim⁡x→∞((x−3)cos⁡(x)x)=⟨−1,1⟩\lim_{x \to \infty}\left(\frac{\left(x - 3\right) \cos{\left(x \right)}}{x}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=⟨−1,1⟩xy = \left\langle -1, 1\right\rangle x
Paridad e imparidad de la función
Comprobemos si la función es par o impar mediante las relaciones f = f(-x) и f = -f(-x).
Pues, comprobamos:
(x−3)cos⁡(x)=(−x−3)cos⁡(x)\left(x - 3\right) \cos{\left(x \right)} = \left(- x - 3\right) \cos{\left(x \right)}
- No
(x−3)cos⁡(x)=−(−x−3)cos⁡(x)\left(x - 3\right) \cos{\left(x \right)} = - \left(- x - 3\right) \cos{\left(x \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = y=(x-3)cosx
    © Sr Examen – Калькулятор