The tables below show two functions. for each set of data: a) determine whether the data represents a linear function, exponential function or neither and explain why. x f(x) -2 18 -1 22 0 26 1 30 2 34 x g(x) -2 2 -1 4 0 8 1 16 2 32 rubric: points concept addressed /2 correctly determines whether each table represents linear, exponential or neither /2 correctly explains their answer.

The first table, representing f(x), is linear.  The data have a constant rate of change or slope:
(between the first two points):  m = (y₂ - y₁)/(x₂ - x₁) = (22-18)/(-1--2) = 4/(-1+2) = 4/1 = 4.  The rate of change  between any two points is the same:
(between the last two points):  m = (34-30)/(2-1) = 4/1 = 4.

The second table, representing g(x), is exponential.  The data points are multiplied by the same constant between successive points.  2*2 = 4; 4*2= 8; 8*2 = 16, etc.