#1. feladat: f(x) = 1.5log(x/2)−2 (0,4]-en
x = seq(0,4,0.1) # x = seq(from=0, to=4, by=0.1)
# lusta megoldas, ha benne hagyjuk a 0-t, a szamolt ertekek NA,
# es kimaradnak az abrazolasbol
# alternativ: seq(0.1,4,0.1)
y1 = log(x)
y2 = log(x/2)
y3 = 1.5 * y2
y4 = y3-2
plot(x,y1,type="l",ylim=c(-7,1.5))
lines(x,y2,col="blue",lty=4)
lines(x,y3,col="purple")
lines(x,y4,col="red",pch=5,type="o")
legend(2,-4,c("log(x)","log(x/2)","1.5log(x/2)","1.5log(x/2)-2"),
	lty=c(1,4,1,1),pch=c(NA,NA,NA,5),col=c("black","blue","purple","red"))