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# Identifying Functions

Alignments to Content Standards: F-LE.A.1.b F-LE.A.1.c

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.

ABCD
xyxyxyxy
161716156
2921429228
312328314314
41545642147

## IM Commentary

This task emphasizes the expectation that students know linear functions grow by constant differences over equal intervals and exponential functions grow by constant factors over equal intervals.

## 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".