In this Exploration, you are going to work with general forms of functions identified by patterns in order to discover why certain patterns in the domain of a given function lead to predictable behavior for the values produced in the range.

2. Sum - Constant Second Difference:

A Quadratic Function Statement: For a function f of the form ax2 bx c with domain values k units apart, then the second differences between consecutive f (x) values are constant and equal to 2ak ^2 . To verify the statement above, find the second differences involving f (x) evaluated at x1,x2= (x1 k), x3 =(x1 2k)

Product - Sum: A Logarithmic Function Statement: For a logarithmic function f, multiplying a given domain value by a constant c results in adding a constant to the corresponding range value:

To verify the statement above, find f (x2 ) in terms of f (x1 ) and fill in the statement below Given f (x) =a blog n x, if x2= cx1 , then f (x2 ) ...