Question

Determine whether the table represents a linear or nonlinear function.

Answer 1

The function represented by the table is given by the rate of change of

the x and y-values which are constant indicating a  linear function.

Response:

The statement that could be used to justify that the table represents a linear function is as following;

• The y-values decrease by the same amount

How to determine if a table represents a linear function?

The table of of a linear function is one in which the first difference in

the y-values is constant given that the difference in the x-values are also

constant.

From the table, the first difference between each y-value and the

previous y-value is found as follows;

20 - 35 = -15

5 - 20 = -15

-10 - 5 = -15

While the difference between the corresponding x-values = 1 as follows;

0 - (-1) = 1

1 - 0 = 1

2 - 1 = 1

Therefore;

The (rate of) change in the x and y -values in the table are constant, and

the function is a linear function.

The correct statement is therefore;

• The y-values decrease by the same amount

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