Tarea 1. Gráficas de funciones.

Realiza la gráfica de las siguientes funciones en el intervalo adecuado.

1. \(f(x)=e^x-3x^2=0\) para \(0\leq x \leq 5\)

f_a <- function(x){exp(x)-3*x^2}

x_a <- seq(0, 5, by=0.0001)
y_a <- f_a(x_a)

graf_a <- ggplot()+
  geom_vline(xintercept = 0, linetype="dashed")+ #eje x
  geom_hline(yintercept = 0, linetype="dashed")+ #eje y
  geom_line(aes(x=x_a, y=y_a), color="red", size=1)+
  #coord_fixed(ratio = 1)+ # misma escala en los ejes
  labs(x="x", y="f(x)", title="Primera gráfica")+
  theme_minimal()

ggplotly(graf_a)

2. \(f(x)=\frac{2x^2-8}{x+2}\)

f_b <- function(x){(2*x^2-8)/(x+2)}

x_b <- seq(0, 10, by=0.0001)
y_b <- f_b(x_b)

graf_b <- ggplot()+
  geom_vline(xintercept = 0, linetype="dashed")+ #eje X
  geom_hline(yintercept= 0, linetype="dashed")+ #eje Y
  geom_line(aes(x=x_b, y=y_b), color= "blue", size=1)+
  labs(x="tiempo", y="velocidad", title = "Segunda gráfica")+
  theme_minimal()
ggplotly(graf_b)

c)\(f(x)=\frac{x+1}{x+2}\)

f_c <- function(x){(x+1)/(x+2)}

x_c <- seq(-1, 5, by=0.0001)
y_c <- f_c(x_c)

graf_c <- ggplot()+
  geom_vline(xintercept=0, linetype="continue")+
  geom_hline(yintercept = 0, linetype= "continue")+
  geom_line(aes(x=x_c, y=y_c), color="red",size=1.1)+
  labs(x="tiempo", y="poblacion", title= "Tercera gráfica")+
  theme_minimal()

ggplotly(graf_c)

4. \(f(x)=3x+1\)

f_d <- function(x){3*x+1}

x_d <- seq(0, 5, by=0.0001)
y_d <- f_d(x_d)

graf_d <- ggplot()+
  geom_vline(xintercept=0, linetype="continue")+
  geom_hline(yintercept = 0, linetype= "continue")+
  geom_line(aes(x=x_d, y=y_d), color="red",size=1.1)+
  #coord_fixed(ratio=1)+
  labs(x="tiempo", y="poblacion", title= "Cuarta gráfica")+
  theme_minimal()



ggplotly(graf_d)

5. \(f(x)=x^4-x^3+x^2-x+1\).

f_e <- function(x){x^4+x^3-x+1}

x_e <- seq(-10, 10, by=0.0001)
y_e <- f_e(x_e)

graf_e <- ggplot()+
  geom_vline(xintercept=0, linetype="continue")+
  geom_hline(yintercept = 0, linetype= "continue")+
  geom_line(aes(x=x_e, y=y_e), color="red",size=1)+
  coord_fixed(ratio=0.002)+
  labs(x="tiempo", y="poblacion", title= "Quinta gráfica")+
  theme_minimal()



ggplotly(graf_e)

6. \(f(x)=x\,cos\,x-3x\).

f_l <- function(x){x*cos(x)-3*x}

x_l <- seq(0, 5, by=0.0001)
y_l <- f_l(x_l)

graf_l <- ggplot()+
  geom_vline(xintercept=0, linetype="continue")+
  geom_hline(yintercept = 0, linetype= "continue")+
  geom_line(aes(x=x_l, y=y_l), color="red",size=1)+
  labs(x="tiempo", y="poblacion", title= "Sexta gráfica")+
  theme_minimal()



ggplotly(graf_l)

7. \(f(x)=e^{2x}\).

f_g <- function(x){exp(2*x)}

x_g <- seq(0, 5, by=0.0001)
y_g <- f_g(x_g)

graf_g <- ggplot()+
  geom_vline(xintercept=0, linetype="continue")+
  geom_hline(yintercept = 0, linetype= "continue")+
  geom_line(aes(x=x_g, y=y_g), color="red",size=1)+
  #coord_fixed(ratio=1)+
  labs(x="tiempo", y="poblacion", title= "Séptima gráfica")+
  theme_minimal()

ggplotly(graf_g)

8. \(f(x)=log(e^x+2)\).

f_h <- function(x){log(exp(x+2))}

x_h <- seq(-5, 5, by=0.0001) 
y_h <- f_h(x_h)

graf_h <- ggplot()+
  geom_vline(xintercept=0, linetype="continue")+
  geom_hline(yintercept = 0, linetype= "continue")+
  geom_line(aes(x=x_h, y=y_h), color="red",size=1)+
  #coord_fixed(ratio=1)+
  labs(x="tiempo", y="poblacion", title= "Octava gráfica")+
  theme_minimal()

ggplotly(graf_h)

1. \(f(x) = cos \,x+sen\,x\).

f_i <- function(x){cos(x)+sin(x)}

x_i <- seq(0, 5, by=0.0001)
y_i <- f_i(x_i)

graf_i <- ggplot()+
  geom_vline(xintercept=0, linetype="continue")+
  geom_hline(yintercept = 0, linetype= "continue")+
  geom_line(aes(x=x_i, y=y_i), color="red",size=1)+
  #coord_fixed(ratio=1)+
  labs(x="tiempo", y="poblacion", title= "Novena gráfica")+
  theme_minimal()

ggplotly(graf_i)

10. \(f(x)=sen(e^x-2)\).

f_j <- function(x){sin(exp(x-2))}

x_j <- seq(0, 5, by=0.0001)
y_j <- f_j(x_j)

graf_j <- ggplot()+
  geom_vline(xintercept=0, linetype="continue")+
  geom_hline(yintercept = 0, linetype= "continue")+
  geom_line(aes(x=x_j, y=y_j), color="red",size=1)+
  #coord_fixed(ratio=1)+
  labs(x="tiempo", y="poblacion", title= "Décima gráfica")+
  theme_minimal()

ggplotly(graf_j)