# 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.

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

## 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".