Question

an air - conditioning company sets a cost for a house call and charges per hour for repair. the company uses the function (f(t)=105t + 98) as the total cost. the number of hours worked is (t) and the total cost is (f(t)). which statement represents the meaning of each part of the function? which part of the function is impacted by an increase of $12 for the net cost? function meaning: the cost for the house call is 105 dollars and the cost per hour is 98 dollars. part impacted: the cost for the house call increases. function meaning: the cost for the house call is 98 dollars and the cost per hour is 105 dollars. part impacted: the cost per hour increases. function meaning: the cost for the house call is 105 dollars and the cost per hour is 98 dollars. part impacted: the cost per hour increases. function meaning: the cost for the house call is 98 dollars and the cost per hour is 105 dollars. part impacted: the cost for the house call increases.

Explanation:

Step1: Analyze the linear - function form

The cost function is \(f(t)=105t + 98\), which is in the form \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept). In the context of cost, \(m\) is the cost per hour and \(b\) is the fixed cost (house - call cost). Here, the cost per hour is \(105\) dollars and the house - call cost is \(98\) dollars.

Step2: Consider the impact of an increase in net cost

An increase in the net cost due to a change in the cost structure. If there is an increase in the cost, and since the house - call cost is the fixed part of the cost and the cost per hour is the variable part, an increase in the net cost related to the fixed cost will impact the house - call cost.

Answer:

Function Meaning: The cost for the house call is 98 dollars and the cost per hour is 105 dollars.
Part Impacted: The cost for the house call increases.