83 Tee (CsT Sequences and Functions Question 29 of 25
Decide whether the data in the table represent a linear function or an
exponential function Explain how you know.
A
4
2
3
14
-23
32
OAThe data represent an exponential function because there is a
OB. The data represent a linear function because there is a common
OC. The data represent an exponential function because there is a
Common ratio of 4.
difference of 9.
Common ratio of -
5
OD. The data represent a linear function because there is a common
difference of -9.

The common difference is same = d = -9

Therefore, the data represent a linear function.

Step-by-step explanation:

Given the table

x                        y

1                         4

2                        -5

3                        -14

4                        -23

5                         -32

Finding the common difference between all the adjacent terms of y-values

d = -5 - 4 = -6,

d = -14 - (-5) = -14+5 = -9

d = -23 - (-14) = -23 + 14 = -9

d = -32 - (-23) = -32 + 23 = -9

It is clear that the common difference between all the adjacent terms is same.

Thus,

d = -9

We know that when y varies directly with x, the function is a linear function.

Here, it is clear that each x value varies 1 unit, and each y value varies -9 units.

i.e. The common difference is same = d = -9

Therefore, the data represent a linear function.