Explain two assumptions of linear extrapolation. (4 marks)DICT MOD 1 July 2020

Linear extrapolation is a method of estimating the value of a function at a point outside the range of known data points. It is based on the assumption that the function is a straight line beyond the range of known data points. There are two main assumptions of linear extrapolation:

1. The function is a straight line: Linear extrapolation assumes that the function is a straight line beyond the range of known data points. This means that the relationship between the variables in the function is linear, or that the change in one variable is proportional to the change in the other variable. This assumption is necessary for linear extrapolation to be accurate, as it allows us to use the known data points to fit a straight line to the data and then use this line to estimate the value at the desired point outside the range of known data points.
2. The function is continuous: Linear extrapolation also assumes that the function is continuous beyond the range of known data points. This means that there are no sudden changes or discontinuities in the function beyond the range of known data points. This assumption is necessary because it allows us to use the known data points to estimate the value of the function at the desired point outside the range of known data points without worrying about sudden changes or discontinuities in the function.