given a table of values for a function, f(x), explain how to determine if f(x) is linear or non linear from the average rate of change.

Linear
functions are functions whose average rate of change is constant. (The constant rate of change
is called the slope.)

Given a table of values, choose any two points and
compute the averate rate of change: `m=(y_2-y_1)/(x_2-x_1)=(Delta y)/(Delta x)` . Then do the
same for any other pair of points. If the function is linear the rate of change will be the same
regardless of the pairs of points you pick.

** If the x's are seperated by
the same amount, you can use the method of finite differences. See link **

href="https://en.wikipedia.org/wiki/Finite_difference">https://en.wikipedia.org/wiki/Finite_difference
href="https://en.wikipedia.org/wiki/Linear_equation">https://en.wikipedia.org/wiki/Linear_equation