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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?

Respuesta :

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]