Chapter 9.7, Problem 1P

A small-order coffee company charges $12 for each bag of coffee plus $3 shipping no matter how many bags are ordered. Describe a function that this situation gives rise to. Make a table for this function, sketch a graph of this function, and fund an equation for this function. Is the function linear or not? How can you tell?

To determine

To find: The function, make table for the function, sketch a graph of the function, also find the equation of function and also check whether the function is linear or not.

Answer to Problem 1P

The equation of the function is $y=12x+3$ and it is a linear function.

Explanation of Solution

Given information:

The cost of each bag of coffee plus is $12 and $3 shipping charges no matter how many bags are order.

Calculation:

The above problem gives rise to a coffee bag function.

The input of the function is the number of bags of coffee ordered and output of the function is charges charged by the coffee company.

Consider $x$ as a input function and $y$ as a output function.

The table represent the given coffee bag function as shown in Table 1

  

The number of coffee bags ordered is represented on $x$ axis and corresponding charge charged by the coffee company on the $y$ axis.

The point obtained from the Table 1 marked on the coordinate and join them.

The graph represented the given coffee bag function is shown in Figure 1.

  

It is observed from the Figure 1 that the total charges charge by the company is the sum of cost of each coffee bag $12x$ and shipping charge $3.

Therefore, the equation of the given coffee bag function can be obtained as,

  $y=12x+3$ .

The above equation is linear function because the graph of linear function is a line.

Therefore, the equation of the function $y=12x+3$ is linear.

Conclusion:

Thus, the equation of the function is $y=12x+3$ and it is a linear function.