## 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".

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