Chapter 8.9, Problem 4CE

To determine

To find: the program that estimate for $y=f\left(x\right)$ and it is define to enter a rule for the function.

Answer to Problem 4CE

#def extrapolate(d, x): 
    y = (d[0][1] + (x - d[0][0]) / 
        (d[1][0] - d[0][0]) * 
        (d[1][1] - d[0][1]));  
  
    return y;  
  
# Driver Code  
  
# Sample dataset  
d = [[ 1.2, 2.7 ], [1.4, 3.1 ]];  
  
# Sample x value  
x = 2.1;  
  
# Finding the extrapolation  
print("Value of y at x = 2.1 :",  
             extrapolate(d, x));  

Explanation of Solution

Given information:

Linear interpolation.

Calculation:

def extrapolate(d, x): 
    y = (d[0][1] + (x - d[0][0]) / 
        (d[1][0] - d[0][0]) * 
        (d[1][1] - d[0][1]));  
  
    return y;  
  
# Driver Code  
  
# Sample dataset  
d = [[ 1.2, 2.7 ], [1.4, 3.1 ]];  
  
# Sample x value  
x = 2.1;  
  
# Finding the extrapolation  
print("Value of y at x = 2.1 :",  
             extrapolate(d, x));