Mathematics: Select the correct statement about the function represented by the table.1 26 2 44 3 62 4 80 5 98A. It is an exponential function because the factor between each x-and y-value is constant.OB. It is a linear function because the y-values increase by an equaldifference over equal intervals of x-values.C. It is a linear function because the difference y - x for each row isconstant.+ PREVIOUS

Select the correct statement about the function

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22.01.2022

Option "B. It is a linear function because the y-values increase by an equal difference over equal intervals of x-values" is the correct answer

Step-by-step explanation:

First of all we have to check the function for linear or exponential.

To check for exponential function, we have to find the factor between y values and x values that is:

$factor = \frac{y}{x}$

So,

For x=1

$\frac{26}{1} = 26\\\frac{44}{2} = 22\\\frac{62}{3} = 20.6$

The function is not an exponential function because the factor between each x-value and y-value is not same.

Now,

Let us find the difference between x-values and y-values

Let

$x_1 = 1\\x_2 = 2\\x_3 = 3\\x_4 = 4\\and\\y_1 = 26\\y_2 = 44\\y_3 = 62\\y_4 = 80$

So for x-values

$x_2-x_1 = 2-1 = 1\\x_3-x_2 = 3-2 = 1\\x_4 - x_3 = 4-3 = 1$

And

$y_2 - y_1 = 44-26 = 18\\y_3 - y_2 = 62-44 = 18\\.\\.\\.$

As we can see that the y-values increase by an equal difference over equal intervals of x-values so the function is a linear function.

Hence,

Option "B. It is a linear function because the y-values increase by an equal difference over equal intervals of x-values" is the correct answer

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