Question

Determine weather each table represents a linear, quadratic, or exponential function.

Answer 1

A: Exponential

B: Quadratic

C: Linear

Explanation:

Solution:-

- We will closely inspect each Table and find the difference between each "Y" value at every unit increase in "x" value:

Table A:

X Y ΔY/ΔX

1 5 xxxxxx Exponential because [ ΔY/ΔX ]

2 11 11 - 5 = 6 increases at the fastest rate out of all

3 29 29 - 11 = 18 functions.

4 83 83 - 29 = 54

5 245 254 - 83 = 171

6 731 731 - 254 = 477

Table B:

X Y ΔY/ΔX Δ^2Y/ΔX^2

0 5 xxxxxx xxx Quadratic because

1 7 7 - 5 = 2 xxx Δ^2Y/ΔX^2 is a constant

2 13 13 - 7 = 6 6-2 = 4 for all quadratic functions

3 23 23 - 13 = 10 10-6 = 4

4 37 37 - 23 = 14 14-10 = 4

5 55 55 - 37 = 18 18-14 = 4

Table C:

X Y ΔY/ΔX

3 20 xxxxxx Linear because

6 18 2 / 3 ΔY/ΔX is a constant

9 16 2 / 3 for all linear functions

15 12 2 / 3

27 4 8/12 = 2/3

39 -4 8/12 = 2/3