3. Funciones en R, graficando las asíntotas de una función
Facultad de Economía, UNAM
Profesor: Cesar Gerardo Hernández Vargas
28/10/2020
library(tidyverse)## ── Attaching packages ───────────## ✓ ggplot2 3.3.1 ✓ purrr 0.3.4
## ✓ tibble 3.0.1 ✓ dplyr 1.0.0
## ✓ tidyr 1.1.0 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0## ── Conflicts ────────────────────
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()1. Graficando asíntotas de una función
Definimos un dominio x para nuestras funciones
x<-seq(-5, 5, 0.1)
x## [1] -5.0 -4.9 -4.8 -4.7 -4.6 -4.5 -4.4 -4.3 -4.2 -4.1 -4.0 -3.9 -3.8 -3.7 -3.6
## [16] -3.5 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1
## [31] -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 -1.3 -1.2 -1.1 -1.0 -0.9 -0.8 -0.7 -0.6
## [46] -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
## [61] 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4
## [76] 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9
## [91] 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0Definimos f(x): f(x)=1/x
fx<-1/x
fx## [1] -0.2000000 -0.2040816 -0.2083333 -0.2127660 -0.2173913 -0.2222222
## [7] -0.2272727 -0.2325581 -0.2380952 -0.2439024 -0.2500000 -0.2564103
## [13] -0.2631579 -0.2702703 -0.2777778 -0.2857143 -0.2941176 -0.3030303
## [19] -0.3125000 -0.3225806 -0.3333333 -0.3448276 -0.3571429 -0.3703704
## [25] -0.3846154 -0.4000000 -0.4166667 -0.4347826 -0.4545455 -0.4761905
## [31] -0.5000000 -0.5263158 -0.5555556 -0.5882353 -0.6250000 -0.6666667
## [37] -0.7142857 -0.7692308 -0.8333333 -0.9090909 -1.0000000 -1.1111111
## [43] -1.2500000 -1.4285714 -1.6666667 -2.0000000 -2.5000000 -3.3333333
## [49] -5.0000000 -10.0000000 Inf 10.0000000 5.0000000 3.3333333
## [55] 2.5000000 2.0000000 1.6666667 1.4285714 1.2500000 1.1111111
## [61] 1.0000000 0.9090909 0.8333333 0.7692308 0.7142857 0.6666667
## [67] 0.6250000 0.5882353 0.5555556 0.5263158 0.5000000 0.4761905
## [73] 0.4545455 0.4347826 0.4166667 0.4000000 0.3846154 0.3703704
## [79] 0.3571429 0.3448276 0.3333333 0.3225806 0.3125000 0.3030303
## [85] 0.2941176 0.2857143 0.2777778 0.2702703 0.2631579 0.2564103
## [91] 0.2500000 0.2439024 0.2380952 0.2325581 0.2272727 0.2222222
## [97] 0.2173913 0.2127660 0.2083333 0.2040816 0.2000000Graficando f(x):
plot(x,fx, type="o", col = "darkgreen")
Graficando las asíntotas de f(x):
plot(x,fx, type="o", col = "darkgreen") + abline(h = 0, v = 0, col = "red")
## integer(0)Definimos g(x): g(x)=(2*x^2)/(x^2-4)
gx<-(2*x^2)/(x^2-4)
gx## [1] 2.380952381 2.399800100 2.420168067 2.442233278 2.466200466
## [6] 2.492307692 2.520833333 2.552104900 2.586510264 2.624512100
## [11] 2.666666667 2.713648528 2.766283525 2.825593395 2.892857143
## [16] 2.969696970 3.058201058 3.161103048 3.282051282 3.426024955
## [21] 3.600000000 3.814058957 4.083333333 4.431610942 4.898550725
## [26] 5.555555556 6.545454545 8.201550388 11.523809524 21.512195122
## [31] Inf -18.512820513 -8.526315789 -5.207207207 -3.555555556
## [36] -2.571428571 -1.921568627 -1.463203463 -1.125000000 -0.867383513
## [41] -0.666666667 -0.507836991 -0.380952381 -0.279202279 -0.197802198
## [46] -0.133333333 -0.083333333 -0.046035806 -0.020202020 -0.005012531
## [51] 0.000000000 -0.005012531 -0.020202020 -0.046035806 -0.083333333
## [56] -0.133333333 -0.197802198 -0.279202279 -0.380952381 -0.507836991
## [61] -0.666666667 -0.867383513 -1.125000000 -1.463203463 -1.921568627
## [66] -2.571428571 -3.555555556 -5.207207207 -8.526315789 -18.512820513
## [71] Inf 21.512195122 11.523809524 8.201550388 6.545454545
## [76] 5.555555556 4.898550725 4.431610942 4.083333333 3.814058957
## [81] 3.600000000 3.426024955 3.282051282 3.161103048 3.058201058
## [86] 2.969696970 2.892857143 2.825593395 2.766283525 2.713648528
## [91] 2.666666667 2.624512100 2.586510264 2.552104900 2.520833333
## [96] 2.492307692 2.466200466 2.442233278 2.420168067 2.399800100
## [101] 2.380952381Graficando g(x):
plot(x,gx, type="o", col = "blue")
Graficando las asíntotas de g(x):
plot(x,gx, type="o", col = "blue") + abline(h = 1, v = c(-2,2), col = "red")
## integer(0)Definimos h(x): h(x)=f(x)/g(x)
hx<-gx/fx
hx## [1] -1.190476e+01 -1.175902e+01 -1.161681e+01 -1.147850e+01 -1.134452e+01
## [6] -1.121538e+01 -1.109167e+01 -1.097405e+01 -1.086334e+01 -1.076050e+01
## [11] -1.066667e+01 -1.058323e+01 -1.051188e+01 -1.045470e+01 -1.041429e+01
## [16] -1.039394e+01 -1.039788e+01 -1.043164e+01 -1.050256e+01 -1.062068e+01
## [21] -1.080000e+01 -1.106077e+01 -1.143333e+01 -1.196535e+01 -1.273623e+01
## [26] -1.388889e+01 -1.570909e+01 -1.886357e+01 -2.535238e+01 -4.517561e+01
## [31] -Inf 3.517436e+01 1.534737e+01 8.852252e+00 5.688889e+00
## [36] 3.857143e+00 2.690196e+00 1.902165e+00 1.350000e+00 9.541219e-01
## [41] 6.666667e-01 4.570533e-01 3.047619e-01 1.954416e-01 1.186813e-01
## [46] 6.666667e-02 3.333333e-02 1.381074e-02 4.040404e-03 5.012531e-04
## [51] 0.000000e+00 -5.012531e-04 -4.040404e-03 -1.381074e-02 -3.333333e-02
## [56] -6.666667e-02 -1.186813e-01 -1.954416e-01 -3.047619e-01 -4.570533e-01
## [61] -6.666667e-01 -9.541219e-01 -1.350000e+00 -1.902165e+00 -2.690196e+00
## [66] -3.857143e+00 -5.688889e+00 -8.852252e+00 -1.534737e+01 -3.517436e+01
## [71] Inf 4.517561e+01 2.535238e+01 1.886357e+01 1.570909e+01
## [76] 1.388889e+01 1.273623e+01 1.196535e+01 1.143333e+01 1.106077e+01
## [81] 1.080000e+01 1.062068e+01 1.050256e+01 1.043164e+01 1.039788e+01
## [86] 1.039394e+01 1.041429e+01 1.045470e+01 1.051188e+01 1.058323e+01
## [91] 1.066667e+01 1.076050e+01 1.086334e+01 1.097405e+01 1.109167e+01
## [96] 1.121538e+01 1.134452e+01 1.147850e+01 1.161681e+01 1.175902e+01
## [101] 1.190476e+01Graficando h(x):
plot(x,hx, type="o", col = "purple")
Graficando las asíntotas de h(x):
plot(x,hx, type="o", col = "purple") + abline(v = c(-2,2), col = "red")
## integer(0)2. Graficando con ggplot2
Creando un data.frame con nuestras variables:
datos<-data.frame(x,fx,gx,hx)
datos## x fx gx hx
## 1 -5.0 -0.2000000 2.380952381 -1.190476e+01
## 2 -4.9 -0.2040816 2.399800100 -1.175902e+01
## 3 -4.8 -0.2083333 2.420168067 -1.161681e+01
## 4 -4.7 -0.2127660 2.442233278 -1.147850e+01
## 5 -4.6 -0.2173913 2.466200466 -1.134452e+01
## 6 -4.5 -0.2222222 2.492307692 -1.121538e+01
## 7 -4.4 -0.2272727 2.520833333 -1.109167e+01
## 8 -4.3 -0.2325581 2.552104900 -1.097405e+01
## 9 -4.2 -0.2380952 2.586510264 -1.086334e+01
## 10 -4.1 -0.2439024 2.624512100 -1.076050e+01
## 11 -4.0 -0.2500000 2.666666667 -1.066667e+01
## 12 -3.9 -0.2564103 2.713648528 -1.058323e+01
## 13 -3.8 -0.2631579 2.766283525 -1.051188e+01
## 14 -3.7 -0.2702703 2.825593395 -1.045470e+01
## 15 -3.6 -0.2777778 2.892857143 -1.041429e+01
## 16 -3.5 -0.2857143 2.969696970 -1.039394e+01
## 17 -3.4 -0.2941176 3.058201058 -1.039788e+01
## 18 -3.3 -0.3030303 3.161103048 -1.043164e+01
## 19 -3.2 -0.3125000 3.282051282 -1.050256e+01
## 20 -3.1 -0.3225806 3.426024955 -1.062068e+01
## 21 -3.0 -0.3333333 3.600000000 -1.080000e+01
## 22 -2.9 -0.3448276 3.814058957 -1.106077e+01
## 23 -2.8 -0.3571429 4.083333333 -1.143333e+01
## 24 -2.7 -0.3703704 4.431610942 -1.196535e+01
## 25 -2.6 -0.3846154 4.898550725 -1.273623e+01
## 26 -2.5 -0.4000000 5.555555556 -1.388889e+01
## 27 -2.4 -0.4166667 6.545454545 -1.570909e+01
## 28 -2.3 -0.4347826 8.201550388 -1.886357e+01
## 29 -2.2 -0.4545455 11.523809524 -2.535238e+01
## 30 -2.1 -0.4761905 21.512195122 -4.517561e+01
## 31 -2.0 -0.5000000 Inf -Inf
## 32 -1.9 -0.5263158 -18.512820513 3.517436e+01
## 33 -1.8 -0.5555556 -8.526315789 1.534737e+01
## 34 -1.7 -0.5882353 -5.207207207 8.852252e+00
## 35 -1.6 -0.6250000 -3.555555556 5.688889e+00
## 36 -1.5 -0.6666667 -2.571428571 3.857143e+00
## 37 -1.4 -0.7142857 -1.921568627 2.690196e+00
## 38 -1.3 -0.7692308 -1.463203463 1.902165e+00
## 39 -1.2 -0.8333333 -1.125000000 1.350000e+00
## 40 -1.1 -0.9090909 -0.867383513 9.541219e-01
## 41 -1.0 -1.0000000 -0.666666667 6.666667e-01
## 42 -0.9 -1.1111111 -0.507836991 4.570533e-01
## 43 -0.8 -1.2500000 -0.380952381 3.047619e-01
## 44 -0.7 -1.4285714 -0.279202279 1.954416e-01
## 45 -0.6 -1.6666667 -0.197802198 1.186813e-01
## 46 -0.5 -2.0000000 -0.133333333 6.666667e-02
## 47 -0.4 -2.5000000 -0.083333333 3.333333e-02
## 48 -0.3 -3.3333333 -0.046035806 1.381074e-02
## 49 -0.2 -5.0000000 -0.020202020 4.040404e-03
## 50 -0.1 -10.0000000 -0.005012531 5.012531e-04
## 51 0.0 Inf 0.000000000 0.000000e+00
## 52 0.1 10.0000000 -0.005012531 -5.012531e-04
## 53 0.2 5.0000000 -0.020202020 -4.040404e-03
## 54 0.3 3.3333333 -0.046035806 -1.381074e-02
## 55 0.4 2.5000000 -0.083333333 -3.333333e-02
## 56 0.5 2.0000000 -0.133333333 -6.666667e-02
## 57 0.6 1.6666667 -0.197802198 -1.186813e-01
## 58 0.7 1.4285714 -0.279202279 -1.954416e-01
## 59 0.8 1.2500000 -0.380952381 -3.047619e-01
## 60 0.9 1.1111111 -0.507836991 -4.570533e-01
## 61 1.0 1.0000000 -0.666666667 -6.666667e-01
## 62 1.1 0.9090909 -0.867383513 -9.541219e-01
## 63 1.2 0.8333333 -1.125000000 -1.350000e+00
## 64 1.3 0.7692308 -1.463203463 -1.902165e+00
## 65 1.4 0.7142857 -1.921568627 -2.690196e+00
## 66 1.5 0.6666667 -2.571428571 -3.857143e+00
## 67 1.6 0.6250000 -3.555555556 -5.688889e+00
## 68 1.7 0.5882353 -5.207207207 -8.852252e+00
## 69 1.8 0.5555556 -8.526315789 -1.534737e+01
## 70 1.9 0.5263158 -18.512820513 -3.517436e+01
## 71 2.0 0.5000000 Inf Inf
## 72 2.1 0.4761905 21.512195122 4.517561e+01
## 73 2.2 0.4545455 11.523809524 2.535238e+01
## 74 2.3 0.4347826 8.201550388 1.886357e+01
## 75 2.4 0.4166667 6.545454545 1.570909e+01
## 76 2.5 0.4000000 5.555555556 1.388889e+01
## 77 2.6 0.3846154 4.898550725 1.273623e+01
## 78 2.7 0.3703704 4.431610942 1.196535e+01
## 79 2.8 0.3571429 4.083333333 1.143333e+01
## 80 2.9 0.3448276 3.814058957 1.106077e+01
## 81 3.0 0.3333333 3.600000000 1.080000e+01
## 82 3.1 0.3225806 3.426024955 1.062068e+01
## 83 3.2 0.3125000 3.282051282 1.050256e+01
## 84 3.3 0.3030303 3.161103048 1.043164e+01
## 85 3.4 0.2941176 3.058201058 1.039788e+01
## 86 3.5 0.2857143 2.969696970 1.039394e+01
## 87 3.6 0.2777778 2.892857143 1.041429e+01
## 88 3.7 0.2702703 2.825593395 1.045470e+01
## 89 3.8 0.2631579 2.766283525 1.051188e+01
## 90 3.9 0.2564103 2.713648528 1.058323e+01
## 91 4.0 0.2500000 2.666666667 1.066667e+01
## 92 4.1 0.2439024 2.624512100 1.076050e+01
## 93 4.2 0.2380952 2.586510264 1.086334e+01
## 94 4.3 0.2325581 2.552104900 1.097405e+01
## 95 4.4 0.2272727 2.520833333 1.109167e+01
## 96 4.5 0.2222222 2.492307692 1.121538e+01
## 97 4.6 0.2173913 2.466200466 1.134452e+01
## 98 4.7 0.2127660 2.442233278 1.147850e+01
## 99 4.8 0.2083333 2.420168067 1.161681e+01
## 100 4.9 0.2040816 2.399800100 1.175902e+01
## 101 5.0 0.2000000 2.380952381 1.190476e+01Graficando f(x):
grafica_fx<-ggplot() + geom_point(data = datos, aes(x = x, y = fx), color = "darkgreen")
grafica_fx
Graficando las asíntotas de f(x):
grafica_fx + geom_vline(xintercept = 0) + geom_hline(yintercept = 0)
Graficando el polígono de f(x):
poligino_fx<-ggplot() + geom_polygon(data = datos, aes(x = x, y = fx), fill = "darkgreen")
poligino_fx
Graficando g(x):
grafica_gx<-ggplot() + geom_point(data = datos, aes(x = x, y = gx), color = "blue")
grafica_gx
Graficando las asíntotas de g(x):
grafica_gx + geom_vline(xintercept = c(-2,2)) + geom_hline(yintercept = 1)
Graficando el polígono de g(x):
poligino_gx<-ggplot() + geom_polygon(data = datos, aes(x = x, y = gx), fill = "blue") + xlab("Eje x") + ylab("Eje y")
poligino_gx
Graficando h(x):
grafica_hx<-ggplot() + geom_point(data = datos, aes(x = x, y = hx), color = "purple")
grafica_hx
Graficando las asíntotas de h(x):
grafica_hx + geom_vline(xintercept = c(-2,2))
Graficando el polígono de h(x):
poligino_hx<-ggplot() + geom_polygon(data = datos, aes(x = x, y = hx), fill = "purple") + xlab("Eje x") + ylab("Eje y")
poligino_hx
3. Actividad de repaso:
Ingresa a https://rstudio.cloud/project/1833666, sigue las instrucciones y crea tu primer gráfica con la función ggplot.
Esta obra fue generada mediante R en October 28, 2020 y forma parte de las actividades realizadas en las materias de Matemáticas I y Taller III, Facultad de Economía, UNAM. Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-CompartirIgual 4.0 Internacional. Creative Commons (CC).