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?

Answer 1

Answer:

The range of the function is $80\leq y\leq 440$

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:

$y=45x+80$

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,

$y=45(0)+80$

$y=80$

Now substitute x=8 in above function.

$y=45(8)+80$

$y=360+80$

$y=440$

Hence, the range of the function is $80\leq y\leq 440$