x <- seq(0.01, 3, len=199)
plot(x, log(x), col="gray", lwd=3, type="l", ylab="f(x)")
lines(x, x-1, lwd=3, col="red")
points(1, 0, pch=19, col="red")
lines(x, (x - 1) - (x-1)^2, lwd=3, col="blue")