Task
The following tables show the values of linear, quadratic, and exponential functions at various values
of $x$. Indicate which function type corresponds to each table. Justify your choice.
A 

B 

C 

D 

x 
y 
x 
y 
x 
y 
x 
y 
1 
6 
1 
7 
1 
6 
1 
56 
2 
9 
2 
14 
2 
9 
2 
28 
3 
12 
3 
28 
3 
14 
3 
14 
4 
15 
4 
56 
4 
21 
4 
7 
Solution
Consecutive differences in Table A are constant ($96=129=1512=3$), indicating a linear function. Consecutive quotients in Table B are constant ($\frac{14}{7} =\frac{28}{14} =\frac{56}{28}=2$) indicating an exponential function. Similarly the constant quotient for Table D is 1/2. Neither consecutive differences nor quotients are constant in Table C, and its ordered pairs are related by the equation $y=x^2+5$. So, Table A should be labeled "linear", Table B and D, "exponential", and Table C, "quadratic".