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?

Answer:The range of the function is [tex]80\leq y\leq 440[/tex]Step-by-step explanation:Consider the provided information.The plumber charges a fixed cost of $80 plus an additional cost of $45 per hour.Let plumber works for x hours, then the required linear function will be:[tex]y=45x+80[/tex]The plumber works a maximum of 8 hours per day. That means the minimum value of x is 0 and maximum value of x is 8.We need to find the range of the function.Range of the function is the set of y values.Substitute x=0 in above function,[tex]y=45(0)+80[/tex][tex]y=80[/tex]Now substitute x=8 in above function.[tex]y=45(8)+80[/tex][tex]y=360+80[/tex][tex]y=440[/tex]Hence, the range of the function is [tex]80\leq y\leq 440[/tex]