#Problem 1

#definition of a straight line function
y=function(x,m,b) m*x+b

#definition x-Vctor
x_vec=seq(-1,3,0.1)

#definition y-vector
y_vec=y(x_vec,1,0)
#plotting x-vector vs. y-vector
plot(x_vec, y_vec, type="l", col="black", xlab='x',ylab='f(x)=y')

#generating mock data point for 0 <= x <= 2 for 10 equaly spaced points
equ_points=10
mock_vec = rep(NA,10)
x_vec_2 =seq(0,2, 2/(equ_points-1))
mock_vec = rnorm({1:10},mean = x_vec_2, sd =  0.4)
points(x_vec_2,mock_vec, col="red", type="p")

##Problem2
conrel =function(b) b
linrel =function(x,m,b) m*x+b
quarel =function(x,a,m,b) a*x**2 + m*x+b

reso = 10  #the resolution
a_val = seq(-4,4,reso)
m_val = seq(-4,8,reso)
b_val = seq(-2,2,reso)