Question

The daily cost of hiring an electrician, y, to work x
hours on a repair project can be modeled using a linear
function. The electrician charges a fixed cost of $120
plus an additional $25 per hour. The electrician works a
maximum of 9 hours per day.

For one day of work, what is the range of the
function for this situation?

A) 0 ≤ x ≤ 9
B) 0 ≤ x ≤ 345
C) 0 ≤ y ≤ 9
D) 120 ≤ y ≤ 345

Answer 1

Answer:

The range of the function is $120\leq y\leq 345$ .

Step-by-step explanation:

The electrician charges a fixed cost of 120 rupees and additional 25 rupees per hour. If the cost of hiring an electrician is y and x is the working hours. Then we have the linear model as,

$y=120+25x$

It is also given that the maximum hours of work is 9 hours. That is the maximum value of $x$ is 9.

So for one day of work, the range of the function as $x$ varies from 0 to 9 is,

$\implies 120+0\times 25 \leq y\leq 120+9\times 25\\\\\implies 120 \leq y \leq 120+225\\\\\implies 120\leq y \leq 345$

Hence the option D is the correct choice.