Question

the daily cost of hiring a plumber, y, to work x hours on a repair project can be modeled using a linear function. the plumber charges a fixed cost of $80 plus an additional cost of $45 per hour. the plumber works a maximum of 8 hours per day. for one day of work, what is the range of the function for this situation? a (0 leq x leq 8) b (80 leq y leq 440) c (0 leq x leq 10) d (45 leq y leq 685)

Explanation:

Step1: Determine the linear function

The cost function is \( y = 80 + 45x \), where \( x \) is the number of hours ( \( 0\leq x\leq8 \) ) and \( y \) is the cost.

Step2: Find the minimum value of \( y \)

When \( x = 0 \) (no hours worked), \( y = 80+45\times0 = 80 \).

Step3: Find the maximum value of \( y \)

When \( x = 8 \) (maximum hours worked), \( y = 80 + 45\times8 = 80+360 = 440 \).

Step4: Determine the range

The range of \( y \) is from the minimum cost to the maximum cost, so \( 80\leq y\leq440 \).

Answer:

B. \( 80\leq y\leq440 \)