Chapter 4.2, Problem 2P

(a)

To determine

The function from the relationship given in data.

Explanation of Solution

The given data table is,

  

The data in the table represents the relationship between the input and output.

From the data table, the value of output increases as the input increases and each input is paired with exactly one output therefore the relationshipgiven in the table is a linear function

Words:The output variable 8 plus two times the input variable.

Equation: $y=8+2x$

Graph:

The graph is shown below:

  

(b)

To determine

To prove: The data of the orderedpairs is to be verified.

Explanation of Solution

The given ordered pairs are,

  $\left(0,2\right),\left(1,4\right),\left(3,5\right),\text{and}\left(1,8\right)$

The function is a relationship between the input and output variable and each input value pairs with exactly one output but in the given pairs for input, there are two output values (4, 8).

Thereforethe set of ordered pairs does not represent a linear function