fx <- function(x){x^4-x^2+6}
sfx <- function(x){12/(abs(x)+1)}
gx <- function(x){1/2*cos(6*x)+7/2}

plot(gx,-2,2,xlim=c(-7,7),ylim=c(0,7),xlab="",ylab="")
par(new=T)
plot(sfx,-7,-1,xlim=c(-7,7),ylim=c(0,7),axes=F,xlab="",ylab="")
par(new=T)
plot(sfx,1,7,xlim=c(-7,7),ylim=c(0,7),axes=F,xlab="",ylab="")
par(new=T)
plot(fx,-1,1,xlim=c(-7,7),ylim=c(0,7),axes=F,xlab="",ylab="")

gx <- function(x){
x[-2>x | x>2] <-NA
1/2*cos(6*x)+7/2
}

fx <- function(x){
x[x<(-1)] <- NA
x[x>1] <- NA
x^4-x^2+6
}

fx <- function(x){
x[-1<x & x<1] <-NA
12/(abs(x)+1)
}

ggplot(data.frame(x=c(-7,7),y=0), aes(x,y))+stat_function(fun=gx) \
+stat_function(fun=fx)+stat_function(fun=sx)