Question

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.

Answer 1

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.