# y4 = f(x) = 2 cos(2x) - 1, [0, 4pi]-n
# fuggvenytrafo, 4 lepesben
x <- seq(0,4*pi,pi/64)
y1 <- cos(x)
y2 <- cos(2*x)
y3 <- 2 * y2
# vagy: y3 <- 2* cos(2*x)
y4 <- y3 - 1
# vagy: y4 <- 2*cos(2*x) -1
plot(x,y1,type="l",ylim=c(-3,2),xlim=c(0,5*pi))
# ylim: y tengelyen abrazolasi tartomany
lines(x,y2,type="o",col="blue",pch=2)
lines(x,y3,col="purple",lty=3)
lines(x,y4,col="red")
legend(4*pi,2,
	c("cos(x)","cos(2x)","2cos(2x)","2cos(2x)-1"),
	col=c("black","blue","purple","red"),
	lty=c(1,1,3,1),
	pch=c(NA,2,NA,NA))