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Identifying Functions


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

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.

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".