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 ($9-6=12-9=15-12=3$), 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".
