Question

In which table is y a linear function of x

Answer 1

We conclude that the table C represents a constant change in x and y.

Hence, table C represents that y is a linear function of x.

Explanation:

Here are some of the rules using which we can easily figure out the true nature of a function.

Linear Function:

The constant change in x and y

Quadratic Function:

The constant change in x

The constant 2nd differences in y

Exponential Function:

The constant change in x

The constant ratio in y

We have to find a table in which y is a linear function of x.

Checking the table C

x -1 0 1 2 3

y 6 8 10 12 14

Here:

There is a constant change in x.

i.e. 0 - (-1) = 1; 1 - 0 = 1; 2 - 1 = 1; 3 - 2 = 1

Also there is a constant change in y.

i.e. 8 - 6 = 2; 10 - 8 = 2; 12 - 10 = 2; 14 - 12 = 2

Thus, we conclude that the table C represents a constant change in x and y.

Hence, table C represents that y is a linear function of x.