Question

an air conditioning company set 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 set 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 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.

• 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.

Explanation:

Step1: Analyze the function \( f(t) = 105t + 98 \)

In a linear function of the form \( y = mx + b \), \( m \) is the slope (rate of change) and \( b \) is the y - intercept (initial value). Here, \( t \) is the number of hours worked. So, the cost per hour is the coefficient of \( t \), which is 105 dollars per hour, and the house call cost (a fixed cost, initial cost) is the constant term 98 dollars.

Step2: Analyze the impact of increasing the set cost

The set cost is the fixed cost, which is the constant term (98) in the function. If the set cost (fixed cost) increases by 12 dollars, the constant term in the function will increase. So the part of the function impacted is the constant term (house call cost part).

Now let's analyze each option:

• Option 1: Incorrect function meaning (swapped cost per hour and house call cost).
• Option 2: Incorrect function meaning (swapped cost per hour and house call cost) and incorrect part impacted (cost per hour is the coefficient of \( t \), not impacted by set cost change).
• Option 3: Correct function meaning (house call cost is 98, cost per hour is 105) and correct part impacted (house call cost (constant term) increases).
• Option 4: Incorrect part impacted (cost per hour is not impacted by set cost change).

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.