# Michael Minn 2/25/2018

# Linear

x = 0:20
y = (x * 5) + 10

plot(x, y, type='l', 
	col="navy", lwd=3,
	las=1, fg="white", font.lab=2, 
	xaxs='i', yaxs='i',
	xlim=c(0, 20), ylim=c(0,120),
	panel.first = grid(nx=NA, ny=NULL, lty=1, col="gray"),
	xlab="x", ylab="y")

text(5, 90, "y = (x * 5) + 10")
abline(a=0, b=0, lwd=3)

# Exponential

x = 0:20
y = 1.2^x

plot(x, y, type='l', 
	col="navy", lwd=3,
	las=1, fg="white", font.lab=2, 
	xaxs='i', yaxs='i',
	xlim=c(0, 20), ylim=c(0,40),
	panel.first = grid(nx=NA, ny=NULL, lty=1, col="gray"),
	xlab="x", ylab="y")

text(5, 35, expression(y == 1.2^x))
abline(a=0, b=0, lwd=3)

# Logarithmic

x = seq(1,20,0.1)
y = log(x)

plot(x, y, type='l', 
	col="navy", lwd=3,
	las=1, fg="white", font.lab=2, 
	xaxs='i', yaxs='i',
	xlim=c(0, 20), ylim=c(0,4),
	panel.first = grid(nx=NA, ny=NULL, lty=1, col="gray"),
	xlab="x", ylab="y")

text(5, 3.5, expression(y == log(x)))
abline(a=0, b=0, lwd=3)

# Sigmoid

x = seq(0,20,0.1)
y = 10 / (1 + exp(-0.6 * (x - 10)))

plot(x, y, type='l', 
	col="navy", lwd=3,
	las=1, fg="white", font.lab=2, 
	xaxs='i', yaxs='i',
	xlim=c(0, 20), ylim=c(0,12),
	panel.first = grid(nx=NA, ny=NULL, lty=1, col="gray"),
	xlab="x", ylab="y")

text(5, 9, expression(y == frac(10, 1 + e^{-0.6 * (x - 10)})))

abline(a=0, b=0, lwd=3)
# Sine

x = seq(0,20,0.1)
y = 5 + 4 * sin(x)

plot(x, y, type='l', 
	col="navy", lwd=3,
	las=1, fg="white", font.lab=2, 
	xaxs='i', yaxs='i',
	xlim=c(0, 20), ylim=c(0,10),
	panel.first = grid(nx=NA, ny=NULL, lty=1, col="gray"),
	xlab="x", ylab="y")

text(5, 9, expression(y == 5 + (4 * sin(x))))

abline(a=0, b=0, lwd=3)